FUNDAMENTALS OF MATERIALS MODELLING FOR HOT …The aim of this study is to develop the fundamentals...

FUNDAMENTALS OF MATERIALS MODELLING

FOR HOT STAMPING OF UHSS PANELS WITH

GRADED PROPERTIES

by

NAN LI

A thesis submitted for the degree of Doctor of Philosophy of Imperial College London

and the Diploma of Imperial College London

Department of Mechanical Engineering

Imperial College London

November 2013

I

DECLARATION OF AUTHORSHIP

I, Nan Li, declare that the work presented in this thesis titled ‘fundamentals of materials

modelling for hot stamping of UHSS panels with graded properties’ is my own, all else is

appropriately referenced.

The copyright of this thesis rests with the author and is made available under a Creative

Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy,

distribute or transmit the thesis on the condition that they attribute it, that they do not use it for

commercial purposes and that they do not alter, transform or build upon it. For any reuse or

redistribution, researchers must make clear to others the licence terms of this work.

II

ABSTRACT

The aim of this study is to develop the fundamentals of materials modelling to enable effective

process control of hot stamping for forming UHSS panels with graded properties for optimised

functional performance. A selective heating and press hardening strategy is adopted to grade the

microstructural distribution of a press hardened component through differential heat treatment of

the blank prior to forming. Comprehensive material models, to enable prediction of austenite

formation and deformation behaviours of boron steel under hot forming conditions, as well as the

dynamic response of a press hardened part with tailored properties in collision situations, have

been developed based on experimental investigations and mechanism studies. The research work

is concerned with four aspects: feasibility of the selective heating and press hardening strategy,

austenite formation in boron steel during selective heating, thermo-mechanical properties of

boron steel under hot stamping, and mechanical properties of boron steel with various

microstructures at room temperature.

Feasibility studies for the selective heating and press hardening strategy were carried out through

a designed experimental programme. A lab-scale demonstrator part was designed and relevant

manufacturing and property-assessment processes were defined. A heating technique and

selective-heating rigs were designed to enable certain microstructural distributions in blanks to be

obtained. A hot stamping tool set was designed for forming and quenching the parts. Test pieces

were formed under various heating conditions to obtain demonstrator parts having variously

graded microstructures. Microstructural distributions in the as-formed parts were determined

through hardness testing and microstructural observation. Ultimately, the structural performance

of the parts was evaluated through bending tests.

III

Heat treatment tests were performed to study the formation of austenite in boron steel during

selective heating. Characterisation of the effects of heating rate and temperature on

transformation behavior was conducted based on the test results. A unified austenite formation

model, capable of predicting full or partial austenite formation under both isothermal and non-

isothermal conditions, was developed, and determined from the heat treatment test results.

Hot tensile tests were performed to study the thermo-mechanical properties of the austenite and

initial phase (ferrite and pearlite) of boron steel. The viscoplastic deformation behaviours of the

both phase states were analysed in terms of strain rate and temperature dependence based on the

test results. A viscoplastic-damage constitutive model, capable of describing the thermo-

mechanical response of boron steel in a state corresponding to hot stamping after selective

heating, was proposed. Values of constants in the model for both the austenite and initial phase

were calibrated from the hot tensile test results.

Dynamic and quasi-static tensile testes combined with hardness testing and microstructural

observation were carried out to study the mechanical properties of press hardened boron steel

with various microstructures at room temperature. Based on the results, the strain rate sensitivity

of the martensite and initial phase of boron steel was characterised; the relationships between

mechanical properties (true ultimate tensile strength, 0.2% proof stress, elongation, and hardness)

and phase composition (volume fraction of martensite), for boron steel with various

microstructures, were rationalised. Finally, a viscoplastic-damage constitutive model, capable of

predicting the mechanical response of a press hardened boron steel part with graded properties

being subjected to crash situations in automobiles, were developed, and determined from the test

results.

IV

ACKNOWLEDGEMENTS

First and foremost, I would like to express my deep gratitude to my supervisors Professor

Jianguo Lin and Dr Daniel S. Balint for their continuous guidance, support, and encouragement

throughout my PhD study. Their discipline, expertise, and inspiration have been indispensable to

my growth as a researcher. I am also very grateful to Professor Trevor A. Dean of the University

of Birmingham for his valuable advice and great help on my work, papers, and thesis.

Financial support from the industrial sponsor SAIC Motor UK Technical Centre is acknowledged.

I would like to thank Dr Damian Dry and Mark Hillier of SAIC for their advice on my PhD

project and provision of material. I am also indebted to my previous supervisor Professor Weimin

Gao of Tongji University for facilitating the project and being willing to help all the time.

Financial support from the ‘UK-China Scholarships for Excellence’ scheme is also

acknowledged.

Sincere thanks to the technical staff of Department of Mechanical Engineering, Imperial College

London: Hugh MacGillivray, Dr Leonard Wanigasooriya, Suresh Viswanathan Chettiar, Amit

Choda, and Mark Holloway. Their assistance was important for the success of my experimental

work. Very many thanks to my previous and current colleagues and officemates: Dr Awang Ngah,

Shamsiah, Dr Qian Bai, Dr Jingqi Cai, Guicai Chen, Shouhua Chen, Thomas Dunnett, Xuetao Li,

Dr Ali Mehmanparast, Dr Mohamed Saad Kamel Mohamed, Aditya Narayanan, Dr Panagiotis

Sphicas, Zhutao Shao, Dr Liliang Wang, Yi Wang, Dr Xiaoyu Xi, Dr Haoliang Yang, Kailun

Zheng and all who helped me and encouraged me in any respect during my PhD study. My

special thanks are given to my lovely PhD-Village members: Qi Cao, Lei Ding, Ran Fei, Yeyi

Liu, Yijiang Wu and Lingling Zheng. The four-year journey has not been easy, but I have been

V

lucky to have them accompany. I would also like to express my appreciation to Dr Mengnan

Shen and Xiaofeng Ju for providing me support and strength from China.

Last but not least, I wish to express a heartfelt gratitude to my beloved parents for their endless

trust, understanding, patience, and support. They hope me around, but they set me free and taught

me to be strong. Without this, my PhD would not have been possible. Thank you, my father and

mother, I own you so much.

VI

NOMENCLATURE

α Ferrite

θ Cementite

ψ Initial phase (ferrite and pearlite)

γ Austenite

Ae1, Ae3 Temperature to start and complete austenite formation under

equilibrium conditions, K

Ac1, Ac3 Temperature to start and complete austenite formation during

continuous heating, K

v Relative volume change

vψ0, vψ(T) Relative volume change of the initial phase at 873K and at any

temperature

vγ0, vγ(T) Relative volume change of austenite at 873K and at any temperature

Cψ, Cγ Thermal expansion coefficient of the initial phase and austenite, /K

N Austenite nucleation rate

G Austenite growth rate

R Gas constant, J/ mol·K

T Absolute temperature, K

T Heating rate, K/s

Tx Temperature corresponding to certain volume fraction of austenite, K

VII

e.g. T50% is the temperature when volume fraction of austenite reaches

50%

t Instantaneous time, s (origin: time at temperature of 873K)

tAc1 Time to start austenite formation, s (same origin as t)

tX Time corresponding to certain volume fraction of austenite, s (same

origin as t)

e.g. t80% is the time when volume fraction of austenite reaches 80%

∆t Soaking time increment, s

∆tX1-X2 Time to increase volume fraction of austenite from x1 to x2 during

soaking, s

e.g. Δt80%fs-90%fs is the time to increase volume fraction of austenite from

80% of fs to 90% of fs during soaking

∆t' Time increment during continuous heating, s

∆t'Ac1-X Time increment from starting austenite formation to reaching certain

volume fraction of austenite during continuous heating, s

fM Volume fraction of martensite

fA Volume fraction of austenite

fA

' Extended volume fraction of austenite

fAs Saturated volume fraction of austenite

fP Volume fraction of pearlite

N Nuclei quantity of austenite per unit sample volume

VIII

QN Activation energy related to nucleation of austenite, J/mol

v Volume growth rate of an austenite nucleus

Ve Extended volume of austenite in a unit of real sample volume

Ve Growth rate of the extended volume of austenite

Qv Activation energy related to volume growth of austenite, J/mol

m ,n Parameters related to the impingement mechanism of austenitization

Tm Melting temperature, K

𝜎𝐸, σ Engineering stress and true stress/flow stress, MPa

εE , εT Engineering strain and true strain

εf True strain to failure/elongation

σUTS True ultimate tensile strength, MPa

σ0.2% 0.2% proof stress, MPa

σv Viscous stress, MPa

εT, εT Total (true) strain and total (true) strain rate

εP, εP Plastic (true) strain and plastic(true) strain rate

εE, εE Elastic (true) strain and elastic (true) strain rate

E Young’s modulus of elasticity, MPa

H Isotropic strain hardening, MPa

k Initial yield stress, MPa

ρ Dislocation density

IX

ρ0 Initial dislocation density of material

L Mean dislocation free path

ρ Normalised dislocation density

ω, ω Damage and damage evolution rate

nV Viscous exponent

nR Isotropic hardening exponent

m' Parameter related to strain rate hardening

QE Activation energy related to elastic modulus, J/mol

Qk Activation energy related to initial plastic slip, J/mol

QK, Qn Activation energy related to viscosity , J/mol

QB Activation energy related to isotropic hardening, J/mol

Qβ Activation energy related to damage, J/mol

A Parameter/material constant related to evolution of dislocation density

B Parameter related to isotropic hardening, MPa

C Parameter related to static recovery of dislocation density

K Parameter related to viscous stress, MPa

β Parameter related to damage

A#, B#, C# Material constants

γ#, 𝛽#, ϕ# Material constants

k0, kx, K0, K

x Material constants, MPa

X

m0, n0, 𝑛𝑉0, v0 Material constants

E0 Material constant, MPa

N0, G0 Material constants

XI

CONTENTS

DECLARATION OF AUTHORSHIP..............................................................................................I

ABSTRACT ................................................................................................................................... II

ACKNOWLEDGEMENTS ........................................................................................................... IV

NOMENCLATURE ...................................................................................................................... VI

CONTENTS .................................................................................................................................. XI

LIST OF FIGURES .................................................................................................................. XVII

LIST OF TABLES ................................................................................................................... XXIII

CHAPTER 1 INTRODUCTION ................................................................................................ 1

1.1 Project driving force ............................................................................................................... 1

1.1.1 Automotive industrial background ................................................................................. 1

1.1.2 Hot stamping of automotive UHSS parts ....................................................................... 2

1.1.3 New strategies and challenges in hot stamping .............................................................. 6

1.2 Aim and objectives of research .............................................................................................. 8

CHAPTER 2 HOT STAMPING TECHNOLOGIES AND DEVELOPMENT ....................... 10

2.1 Introduction to hot stamping ................................................................................................ 10

2.1.1 Boron steel – 22MnB5 .................................................................................................. 11

2.1.2 Process parameters ........................................................................................................ 17

2.1.3 Advantages and limitations of conventional hot stamping processes ........................... 19

2.2 Tailored solutions in hot stamping ....................................................................................... 21

2.2.1 Manufacturing of hot stamped parts with tailored properties ....................................... 21

2.2.1.1 Additional operations to hot stamping ................................................................... 21

XII

2.2.1.2 Selective heat treatment strategies integrated in hot stamping .............................. 24

2.2.2 Technologies for process control of thermal conditions ............................................... 27

2.2.2.1 Selective cooling solutions .................................................................................... 27

2.2.2.2 Advanced techniques for selective heating ............................................................ 29

2.2.3 Analysis of the selective heating and press hardening strategy .................................... 32

2.3 Microstructural control during heating ................................................................................. 34

2.3.1 Studies on austenite formation ...................................................................................... 34

2.3.2 Modelling of austenite formation ................................................................................. 35

2.4 Final properties of hot stamped panels ................................................................................. 36

2.5 Summary .............................................................................................................................. 39

CHAPTER 3 FEASIBILITY STUDIES FOR THE SELECTIVE HEATING AND PRESS

HARDENING STRATEGY .......................................................................................................... 41

3.1 Introduction .......................................................................................................................... 41

3.2 Experimental design ............................................................................................................. 41

3.2.1 Concept illustration ....................................................................................................... 41

3.2.2 Material and demonstrator part ..................................................................................... 43

3.2.3 Test programme ............................................................................................................ 43

3.3 Heating technique ................................................................................................................. 44

3.4 Hot stamping ........................................................................................................................ 49

3.4.1 Design of hot stamping tool set .................................................................................... 49

3.4.2 Hot stamping experiments ............................................................................................ 52

3.5 Microstructural distribution analysis .................................................................................... 53

3.5.1 Hardness testing ............................................................................................................ 53

3.5.2 Microstructural observation .......................................................................................... 55

XIII

3.5.3 Discussion ..................................................................................................................... 56

3.6 Structural performance assessment ...................................................................................... 57

3.6.1 Three point bending tests .............................................................................................. 57

3.6.2 Results and discussion .................................................................................................. 57

3.7 Summary .............................................................................................................................. 59

CHAPTER 4 EXPERIMENTAL PROGRAMME OF FUNDAMENTAL TESTS ................. 60

4.1 Introduction .......................................................................................................................... 60

4.2 Austenite formation .............................................................................................................. 60

4.2.1 Test equipment and specimen design ......................................................................... 61

4.2.2 Test programme ............................................................................................................ 63

4.3 Thermo-mechanical properties at elevated temperatures ..................................................... 64

4.3.1 Test equipment and programme ................................................................................... 64

4.3.2 Specimen design and test procedure ............................................................................. 67

4.3.2.1 Specimen design .................................................................................................... 67

4.3.2.2 Temperature gradients in the longitudinal direction ............................................. 67

4.3.2.3 Control of strain rate .............................................................................................. 68

4.4 Mechanical properties at room temperature ......................................................................... 71

4.4.1 The first group: tensile testing over a range of strain rates ........................................... 71

4.4.1.1 Design of experiment and specimen ...................................................................... 72

4.4.1.2 Specimen preparation ............................................................................................ 74

4.4.1.3 Set-up and procedure for quasi-static tensile testing ............................................. 75

4.4.1.4 Set-up and procedure for dynamic tensile testing .................................................. 78

4.4.2 The second group: tensile testing over a series of phase compositions ........................ 81

XIV

4.4.2.1 Specimen design and preparation .......................................................................... 81

4.4.2.2 Test procedure ....................................................................................................... 83

CHAPTER 5 EXPERIMENTAL RESULTS AND DISCUSSION ......................................... 84

5.1 Introduction .......................................................................................................................... 84

5.2 Austenite formation .............................................................................................................. 84

5.2.1 Mechanisms of austenite formation in hypoeutectoid steels ........................................ 85

5.2.2 Experimental results ..................................................................................................... 87

5.2.3 Analysis of full austenite formation .............................................................................. 92

5.2.3.1 Effects of heating rate on non-isothermal austenite formation .............................. 93

5.2.3.2 Effects of heating rate on isothermal austenite formation ..................................... 97

5.2.4 Analysis of intercritical annealing .............................................................................. 101

5.2.4.1 Saturated volume fraction .................................................................................... 101

5.2.4.2 Effects of temperature on isothermal austenite formation ................................... 102

5.3 Thermo-mechanical properties of boron steels under hot stamping conditions ................. 105

5.3.1 Results: flow stress-strain curves ................................................................................ 105

5.3.1.1 Strain rate and temperature dependence of austenite ........................................... 105

5.3.1.2 Strain rate and temperature dependence of initial phase ..................................... 108

5.3.2 Characterisation of flow stress response ..................................................................... 109

5.3.2.1 Effects of strain rate ............................................................................................. 110

5.3.2.2 Effects of temperature .......................................................................................... 112

5.4 Mechanical properties of boron steels at room temperature .............................................. 113

5.4.1 Dynamic tensile behaviour of the martensite and initial phase for boron steel .......... 113

5.4.1.1 Results: flow stress-strain curves ......................................................................... 113

XV

5.4.1.2 Strain rate sensitivity of the phase states ............................................................. 115

5.4.2 Effects of microstructure on tensile behaviour of boron steel .................................... 116

5.4.2.1 Relationships between mechanical properties and phase composition ................ 116

5.4.2.2 Effects of phase composition on tensile properties ............................................. 117

5.5 Summary ............................................................................................................................ 120

CHAPTER 6 MATERIALS MODELLING ........................................................................... 122

6.1 Introduction ........................................................................................................................ 122

6.2 Development of austenite formation model for the boron steel during selective heating .. 122

6.2.1 Model development .................................................................................................... 123

6.2.1.1 Extended volume of austenite .............................................................................. 123

6.2.1.2 Real volume fraction of austenite ........................................................................ 126

6.2.1.3 Saturated volume fraction of austenite ................................................................ 128

6.2.2 Formulation of unified constitutive equations ............................................................ 129

6.2.3 Determination of the equations ................................................................................... 130

6.2.3.1 Calibration of the constants from experimental data ........................................... 130

6.2.3.2 Validation and analysis ........................................................................................ 133

6.3 Viscoplastic-damage constitutive model ............................................................................ 135

6.3.1 Flow rule ..................................................................................................................... 136

6.3.2 Isotropic work hardening ............................................................................................ 138

6.3.3 Evolution of dislocation density ................................................................................. 139

6.3.4 Evolution of damage ................................................................................................... 140

6.3.5 Modified flow rule and Hooke’s law .......................................................................... 142

6.4 Unified viscoplastic-damage constitutive equations for boron steels under hot stamping

conditions ................................................................................................................................. 143

XVI

6.4.1 Formulation of unified viscoplastic-damage constitutive equations .......................... 143


6.4.2.1 Calibration of the constants from experimental data ........................................... 145

6.4.2.2 Analysis on the modelling results ........................................................................ 150

6.5 Unified viscoplastic-damage constitutive equations for multiphase boron steels for

crashworthiness analysis .......................................................................................................... 151

6.5.1 Formulation of unified viscoplastic-damage constitutive equations .......................... 151


6.6 Summary ............................................................................................................................ 155

CHAPTER 7 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK .................. 156

7.1 Conclusions ........................................................................................................................ 156

7.1.1 Feasibility of the selective heating and press hardening strategy ............................... 156

7.1.2 Austenite formation in boron steel during selective heating ...................................... 157

7.1.3 Thermo-mechanical properties of boron steel under hot stamping ............................ 159

7.1.4 Mechanical properties of boron steel with various microstructures at room temperature

............................................................................................................................................. 160

7.2 Suggestions for future work ............................................................................................... 161

REFERENCES ............................................................................................................................ 164

APPENDIX 1 CALCULATION OF AUSTENITE VOLUME FRACTION ............................. 177

APPENDIX 2 STRAIN CORRECTION AT NECKING STAGE ............................................. 180

XVII

LIST OF FIGURES

Figure 1.1 Mechanical properties of boron steel before, during, and after hot stamping, compared

with other types of AHSS steels and Mild steels used for cold forming [15, 27] .......................... 4

Figure 1.2 Forming capabilities of different forming techniques for automotive applications, in

terms of material strength and geometric complexity of formed parts [27] ................................... 5

Figure 1.3 Components manufactured by hot stamping (press hardening) in the Body-in-White

(BIW) of the 3rd generation of the ultra-light Audi A3, utilising different types of steel [30] ....... 6

Figure 2.1 Hot stamping processes: (a) direct method (b) indirect method [53] .......................... 11

Figure 2.2 Experimental data and numerical predictions of 22MnB5 flow behaviours at different

temperatures from 923K to 1173K at the strain rate of (a) 0.1/s and (b) 10/s [22] ....................... 14

Figure 2.3 Experimental (symbols) and numerical predicted (solid curves) flow behaviours of

boron steel (USIBOR 1500P, ArcelorMittal) at (a) different temperatures from 873K to 1073K

(strain rate: 0.1/s) and (b) different strain rates from 0.01/s to 10/s (deformation temperature:

973K) [16] ..................................................................................................................................... 15

Figure 2.4 CCT diagram of a typical 22MnB5 boron steel (USIBOR 1500P, ArcelorMittal) under

the undeformed (solid lines) [24] and deformed (dashed lines) states ......................................... 16

Figure 2.5 Schematic of the typical temperature profile of blanks in hot stamping processes ...... 18

Figure 2.6 Schematics illustrating the manufacturing of hot stamped B-pillars from (a) tailored

welded blanks (TWB) [29, 74], and (b) tailored rolled blanks (TRB) [79, 80] ............................. 22

Figure 2.7 hot stamping of a B-Pillar with graded microstructures by selective heat treatment: (a)

Image of a hot stamped B-pillar being partially hardened [40], with a temperature profile of a

selective cooling process in a continuous cooling transformation (CCT) diagram (b) An as-

formed B-pillar with graded properties, and the typical tensile properties of the martensite and

XVIII

initial phase of boron steel (c) Image of a blank being partially austenitized, with a temperature

profile of a selective heating process in a continuous heating transformation (CHT) diagram .... 25

Figure 2.8 Textures on die surfaces [86] ....................................................................................... 28

Figure 2.9 Principle of selective heating of a steel sheet using bypass resistance heating [35] ... 30

Figure 2.10 Principle of contact heating [90] ................................................................................ 31

Figure 2.11 (a) Ultimate tensile strength (σUTS

) and 0.2% yield stress (σ0.2%

) and (b) Uniform

elongation versus Vickers hardness from the quasi-static tension tests conducted at a strain rate of

0.003 /s (The error bars represent +/- the standard deviation of repeated test results) [37] .......... 38

Figure 3.1 Schematics illustrating the manufacturing process and experimentation for function

assessment (a) Selective heating of the work-piece (b) An as-formed part after hot stamping and

cold die quenching (c) Three point bending of the as-formed part................................................ 42

Figure 3.2 Cross-section of a demonstrator beam (dimensions are in mm) .................................. 43

Figure 3.3 Selective heating technique (a) Set-up of facilities for selective heating and

temperature measurement (b) 3-D diagram of the selective heating rig (c) Location of

thermocouples attached to a work-piece (dimensions in the figure are in mm) ............................ 45

Figure 3.4 Temperature profiles of different positions of a work-piece under selective heating

conditions: (a) S-60mm, (b) S-100mm .......................................................................................... 48

Figure 3.5 Temperature profiles for 4 different test conditions ..................................................... 49

Figure 3.6 Schematics illustrating the working mechanism of the tool set and material flow of the

work-piece (a) Start of forming (b) during forming, middle groove has been formed (c) final

stage of forming ............................................................................................................................. 51

Figure 3.7 Isometric view of the hot stamping and cold die quenching tool set ........................... 51

Figure 3.8 Set-up of facilities for hot stamping experiment .......................................................... 52

Figure 3.9 View of the cross-section of a formed product ............................................................ 53

Figure 3.10 Hardness distribution through a cross-section of an S-320mm as-formed part ......... 54

XIX

Figure 3.11 Hardness distributions along the longitudinal direction of S-60mm and S-100mm as-

formed parts ................................................................................................................................... 55

Figure 3.12 Typical SEM micrographs of boron steel from different microstructure zones

(sampled from flange edge) of an S-100mm as-formed part ......................................................... 56

Figure 3.13 Failure modes under bending for boron steel parts having different microstructural

topographies ................................................................................................................................... 58

Figure 3.14 Load bearing performance of boron steel parts having different microstructural

topographies: (a) Load deflection curve (b) Stroke at the onset of instability against the

proportional length of full martensite phase .................................................................................. 58

Figure 4.1 Gleeble 3800 thermo-mechanical materials simulator ................................................. 61

Figure 4.2 Test set-up and specimen design .................................................................................. 62

Figure 4.3 Test programme of heat treatments with different heating rates and soaking

temperatures ................................................................................................................................... 63

Figure 4.4 Temperature-time profiles for isothermal tensile testing of boron steels in both

austenite (soaked at 1173K) and the initial phase (soaked at 923K) ............................................. 65

Figure 4.5 Specimen design (dimensions are in mm) with schematic dilatometer and three pairs

of thermocouples attached ............................................................................................................. 67

Figure 4.6 Temperature distributions along the specimen in the longitudinal direction at different

testing temperatures ....................................................................................................................... 68

Figure 4.7 Deformation on a fractured specimen .......................................................................... 70

Figure 4.8 Specimen design (dimensions are in mm) with a schematic strain gauge attached ..... 73

Figure 4.9 Set-up of facilities and specimen for low rate tensile testing ....................................... 76

Figure 4.10 Set-up of facilities and specimen for dynamic tensile testing .................................... 77

Figure 4.11 Design of specimens (dimensions are in mm) for quasi-static tensile testing (solid

line) and Gleeble heat treatments (dash line) ................................................................................. 82

XX

Figure 4.12 Test-pieces for different testing .................................................................................. 83

Figure 5.1 The formation of austenite in a hypoeutectoid steel (containing less than 0.76 wt% C)

....................................................................................................................................................... 85

Figure 5.2 Experimental curves showing the width change of specimen against (a) temperature

and (b) time during the heat treatment process (heating rate: 5K/s, soaking temperature: 1173K)

....................................................................................................................................................... 89

Figure 5.3 Width changes of specimens tested at different (a) heating rates (soaking temperature:

1173K), and (b) soaking temperatures (heating rate: 5K/s) ........................................................... 90

Figure 5.4 Variations of volume fraction of austenite with temperature and time for different (a)

heating rates (soaking temperature: 1173K) and (b) soaking temperatures (heating rate: 5K/s) .. 92

Figure 5.5 Continuous heating transformation (CHT) diagram .................................................... 94

Figure 5.6 Effects of heating rate on austenite formation under continuous heating conditions ... 95

Figure 5.7 Effects of heating rate on the transformation time to increase austenite volume fraction

by 5% from 80%, 85% and 90% during soaking at 1173K ........................................................... 98

Figure 5.8 Volume fractions of austenite for different heating rates with time normalised by the

soaking time increments for different austenite volume fractions, during soaking at 1173K ..... 100

Figure 5.9 Saturated volume fractions of austenite at different soaking temperatures ................ 101

Figure 5.10 Effects of soaking temperature on the transformation time to increase austenite

volume fraction by 10% of fAs from 80% of fAs ........................................................................... 103

Figure 5.11 Evolution curves of austenite volume fraction for different temperatures under

isothermal transformation conditions .......................................................................................... 104

Figure 5.12 Experimental flow stress-strain relationships for austenite for different strain rates at

a deformation temperature of 973K ............................................................................................. 105

Figure 5.13 Experimental flow stress-strain relationships for austenite for different deformation

temperatures (designed strain rate: 0.50/s) .................................................................................. 107

XXI

Figure 5.14 Experimental flow stress-strain relationships of the initial phase for different strain

rates at a deformation temperature of 923 K ............................................................................... 108

Figure 5.15 Experimental flow stress-strain relationships of the initial phase for different

deformation temperatures (designed strain rate: 0.50/s) .............................................................. 109

Figure 5.16 Flow stress at different strain levels (0.005, 0.05, and 0.1) for different strain rates

..................................................................................................................................................... 111

Figure 5.17 Flow stress at different strain levels (0.005, 0.05, and 0.1) for different deformation

temperatures (designed strain rate: 0.50/s) .................................................................................. 112

Figure 5.18 True stress-strain curves of the martensite and initial phase of boron steels for

different strain rates tested at room temperature ......................................................................... 114

Figure 5.19 Effects of strain rate (0.001/s, 0.05/s, 5/s, 50/s, 200/s, and 500/s) on the tensile

properties of the martensite and initial phase of the boron steel.................................................. 116

Figure 5.20 The relationships of true ultimate tensile strength and martensite volume fraction

with hardness for heated treated boron steel with various phase compositions .......................... 117

Figure 5.21 True stress-strain curves of heat treated boron steel with various volume fractions of

martensite (quasi-static tests for the strain rate of 0.001/s at room temperature) ........................ 118

Figure 5.22 Effects of martensite volume fraction on tensile properties of heat treated boron

steels (quasi-static tests for the strain rate of 0.001/s at room temperature) ................................ 119

Figure 6.1 Comparison of experimental (symbols) and computed (solid curve) saturated volume

fraction of austenite at intercritical annealing temperatures using equation (6.21) ..................... 131

Figure 6.2 Comparison of experimental (symbols) and numerical integrated (solid curves)

volume fractions of austenite formation under different heating conditions for calibration ....... 132

Figure 6.3 Comparison of experimental (symbols) and predicted (solid curves) volume fractions

of austenite formation for validation (Heating rate: 2K/s, soaking temperature: 1273K) ........... 133

XXII

Figure 6.4 Comparison of experimental (symbols) and predicted (solid curves) continuous

heating transformation (CHT) data, which are shown for different volume fractions of austenite

(10%–70%) with various heating rates (1–25K/s) ....................................................................... 134

Figure 6.5 Comparison of experimental (symbols) and predicted (solid line) relationships of time

increment to attain 80%–90% austenite volume fraction under an isothermal condition (1173K)

with various heating rates (1–25K/s) ........................................................................................... 135

Figure 6.6 Flow stress-strain responses of viscoplastic solids ..................................................... 136

Figure 6.7 Comparison of experimental (symbols) and numerical integrated (solid curves) true

stress-strain curves for austenite at elevated temperatures .......................................................... 148


stress-strain curves for the initial phase at elevated temperatures ............................................... 149


stress-strain curves for boron steels with various phase compositions at room temperature ...... 154

Figure A1.1 Conversion from width change curve to relative volume change curve ................. 178

Figure A2.1 Strain correction method at necking stage ............................................................... 181

Figure A2.2 An example true stress-strain curve showing the correction at necking stage ........ 182

XXIII

LIST OF TABLES

Table 2.1 Chemical composition of a typical 22MnB5 boron steel (mass in % min-max) [55] ... 12

Table 2.2 Mechanical properties of 22MnB5 boron steels [20, 21, 54, 55] .................................. 12

Table 3.1 Chemical composition (Max value - ladle analysis in %) [21]...................................... 43

Table 3.2 Test programme (‘√’ represents the selected test conditions) ....................................... 44

Table 4.1 Test programme (‘√’ represents the selected test conditions) ....................................... 66

Table 4.2 Matrix of test programme and facilities ......................................................................... 74

Table 6.1 Material constants for equations (6.17) – (6.23) .......................................................... 133

Table 6.2 Material constants for equations (6.38) – (6.49) for the austenite and initial phase of

boron steels .................................................................................................................................. 147

Table 6.3 Temperature dependent parameters for the austenite and initial phase of boron steels

..................................................................................................................................................... 150

Table 6.4 Material constants for equations (6.50) – (6.59) .......................................................... 155

1

CHAPTER 1 INTRODUCTION

1.1 Project driving force

1.1.1 Automotive industrial background

A huge global challenge that the modern automotive industry is facing as of today is to improve

energy efficiency and accordingly reduce environmental pollution from vehicle emissions. In the

European Union (EU), to help consumers choose vehicles with low fuel consumption, a directive

1999/94/EC was issued in December 1999, which ensures useful information on fuel

consumption and carbon dioxide (CO2) emissions of new passenger cars is available to potential

buyers [1]. In the United Kingdom, it came into force in November 2001 [2]. Since cars are

responsible for around 12% of total EU emissions of CO2, the main greenhouse gas, EU

legislation adopted in 2009 sets mandatory targets for new cars, to achieve 18% and 40% of

emission reduction by 2015 and 2020 respectively [3]. Also, in the United States, the

Environmental Protection Agency (EPA) and National Highway Traffic Safety Administration

(NHTSA) issued a joint final rule in May 2011, establishing new requirements for a fuel

economy and environment label that is mandatory for all new passenger cars and trucks starting

with model year 2013 [4]. In this context, lightweight technology plays a key role.

Another critical functional element for the design of modern car body structures is safety [5].

Significant steps towards improved protection of occupants of cars have been made since 1990s

[6]. A study in the United Kingdom concluded that improved vehicle crash protection (also

known as passive safety) for car occupants and pedestrians would have the greatest effect, out of

all new policies under consideration, in reducing road casualties in Great Britain [7]. Also, a

review by the European Transport Safety Council estimated that improved standards for crash

2

protection could reduce deaths and serious injuries on European roads by as much as 20% [6]. As

a result, both legislative standards and market forces, produced by different authorities on a

global scale such as the United Nations Economic Commission for Europe, Insurance Institute

for Highway Safety (IIHS) and New Car Assessment Program (NCAP) in the United States, are

making increasingly tight requirements on the vehicle crash protection. The concept of

‘crashworthiness’, termed as the ability of a structure to protect its occupants during an impact,

has been well understood and incorporated into current car design [6]. The most straightforward

and effective solution to improve crashworthiness is increasing the strength and ability to absorb

energy of safety components.

The apparent contradictory requirements for reducing weight and increasing crashworthiness

have greatly stimulated technological innovation in materials and manufacturing processes. As a

consequence, lightweight alloys such as aluminium and magnesium and high yield strength steels

such as advanced high strength steels (AHSS), are being used and accordingly, new forming

techniques, have been significantly developed [8-12]. Nevertheless, steel, because its strength has

been improved at a relatively low cost, is still the dominant material adopted for manufacturing

automobiles nowadays [13, 14].

1.1.2 Hot stamping of automotive UHSS parts

According to metallurgical designation, automotive steels can be classified into [15]:

Low-strength steels (LSS), such as interstitial-free (IF) and mild steels;

Conventional high strength steels (HSS), such as carbon-manganese (CM), bake hard

enable (BH), and high-strength, low-alloy steels (HSLA);

Advanced high strength steels (AHSS), such as dual phase (DP), transformation-induced

plasticity (TRIP), complex phase (CP), and martensitic steels (M).

3

Different from conventional HSS, which are usually hardened by solid solution, precipitation or

grain refining, the AHSS are hardened by phase transformation [16]. For example, martensitic

steel (M) is produced by fast quenching from austenite temperature to obtain lath martensite, and

shows the ultra-high tensile strength level, typically between 900MPa–1500 MPa or even higher

[17]. Normally, this type of steel is termed as ultra-high strength steels (UHSS).

Because of its high yield strength UHSS sheet can be used in thinner gauges than lower strength

steel, whilst retaining structural rigidity and strength. Therefore, it can be used to lighten the

weight of car bodies leading to reduced fuel consumption and enhanced passenger safety.

However, forming UHSS at room temperature is limited by low formability and considerable

spring-back [18, 19].Thereby, hot stamping (also termed as press hardening) of quenchable steel

sheets for ultra-high strength components has been developed and widely used as an effective

solution to the problem.

Boron steel, as an alloy with splendid harden ability, is adopted for press hardening [20]. As

shown in Figure 1.1, the ultimate tensile strength (UTS) and elongation of typical as-delivered

boron steel lie between those of DP 450 and DP 600, which are about 550MPa and 20%,

respectively [21]. When it is heated to full austenitization, the flow stress dramatically drops, and

the ductility jumps to about 40%–50% [22-24]. This enables austenitic boron steel sheets to be

formed with remarkably reduced forming load, consequently minimised spring-back, and greatly

improved formability [18]. By quenching within cold dies in the same operation, the deformed

boron steel transforms from austenitic phase to martensite. Thus, UHSS parts having a tensile

strength of approximately 1500 MPa are obtained [21]. By contrast, for other cold formed AHSS

steels, high forming forces are needed to achieve plastic deformation, and large spring-back and

excessive tool wear arise as a consequence [25, 26]. In addition, due to limited formability,

conventional cold forming of high strength steels is limited to the production of relatively simple

4

geometries [25]. Figure 1.2 summarises the forming capabilities of different forming techniques

used in car body manufacturing, in terms of achievable strength and geometries of formed parts.

Again, hot stamping shows the unmatchable ability to produce highly complicated components

with ultra-high strength.

Figure 1.1 Mechanical properties of boron steel before, during, and after hot stamping, compared

with other types of AHSS steels and Mild steels used for cold forming [15, 27]

5

Figure 1.2 Forming capabilities of different forming techniques for automotive applications, in

terms of material strength and geometric complexity of formed parts [27]

Due to its outstanding advantages, the adoption of hot stamping has been experiencing an

exponential increase, coming from 3 million parts per year in 1987 to 8 million parts per year in

1997 to 95 million parts per year in 2007, and is expected to achieve 450 million parts per year in

2013 [28, 29]. At the same time, as the technology evolved, forming more complex geometries

has been realised. For example, transmission tunnels can be formed by using complex hot

stamping tools with multiple-point hydraulic cushions. Thereby, the number of hot stamped parts

per vehicle has increased from 4 in the 1990s to 20–30 today [28], and 20% body weight of some

vehicles is composed of press hardened steel. One example is the 3rd generation of the Audi A3

developed for ultra-light design in 2012, in which the mass percent of boron steel is 21.7%. The

Body-in-White (BIW) of this model is illustrated in Figure 1.3, showing the hot stamped UHSS

components. These are mainly safety relevant components, such as roof rail reinforcements, sill

reinforcements, and B-pillars. The proportions of different types of automotive steels adopted in

the BIW are also given, where hot stamped UHSS accounts for 26.4%.

6

Figure 1.3 Components manufactured by hot stamping (press hardening) in the Body-in-White

(BIW) of the 3rd generation of the ultra-light Audi A3, utilising different types of steel [30]

1.1.3 New strategies and challenges in hot stamping

Since a car body is a complex structure subject to complicated load situations, increasing the

strength of a whole component uniformly does not always produce the optimum condition

[5].Now, great attention is being paid to developing new strategies in hot stamping, so as to

produce parts with tailored distribution of mechanical properties, which introduces the potential

for making parts conforming more fully to functional requirements [31-33]. For example, in

safety critical beams, instead of utilising a full martensite phase, soft regions of ductile phases,

such as ferrite and pearlite, can be incorporated to enhance energy absorption or tune crash

deceleration pulses [31]. This is a concept about optimising structural performance by means of

microstructural design, which can be realised by controlling thermal conditions, during heating or

quenching, in hot stamping processes. To implement the concept for functional-optimisation-

driven forming, process control analysis based on computer simulation is an invaluable tool and

comprehensive material models to describe the behaviour of boron steel under forming

7

conditions and crash situations in automobiles are vital. To establish material models for

simulation, knowledge of fundamentals of phase transformation kinetics and deformation

mechanisms of boron steel in hot stamping, as well as the mechanical properties of boron steel in

various microstructural states after hot stamping is essential.

In recently years, there has been great interest in forming tailored parts through selective

quenching strategy [12, 34-40]. As a result, extensive studies have been carried out on austenite

decomposition in boron steel during cooling [41, 42]. However, because a long cooling time is

required to achieve ductile phases, there is an intrinsic conflict with the industrial requirement for

short cycle times. This shortcoming can be overcome by another strategy, which is termed as

selective heating and press hardening and is investigated in this study. In the operation, a blank is

heated under tailored thermal conditions, which enables part of the steel to be fully or partially

austenitized and the other part with its phase untransformed. Subsequently, the blank is formed

and quickly quenched in cold dies, as for conventional hot stamping operations. Thus, a part with

graded microstructure can be formed without sacrificing production efficiency, where the

fraction and distribution of martensite in the as-formed part is determined by the extent of

austenitization.

The selective heating and press hardening strategy is a promising technology for hot stamping,

about which systematic studies have not yet been undertaken. Austenite formation in boron steel,

a key aspect of this new strategy, has not drawn much attention compared with its decomposition

[43, 44]. In addition, deformation in this strategy involves boron steel in various phase states

rather than only austenite, as in the conventional process, yet no published work on the thermo-

mechanical properties of boron steel in ferritic/pearlitic state under hot stamping conditions has

been found. Therefore, there is large gap of knowledge to fill for the effective control of the

selective heating and press hardening process. Moreover, only few studies have been conducted

8

on the mechanical properties of as-formed boron steels [45, 46], and a literature search has

revealed no developed material model or characterisation linked to heating condition. An

efficient structural optimisation cannot be realised unless the relationship between mechanical

properties of as-formed boron steels and the corresponding microstructures achieved by certain

thermal conditions is quantitatively determined.

1.2 Aim and objectives of research

The aim of this research is to develop fundamental material models, to enable effective process

control of hot stamping, by adopting selective heating and press hardening strategy, for forming

UHSS panels with graded properties for optimised functional performance. To realise this goal,

four objectives need to be achieved:

Validate the selective heating and press hardening strategy and demonstrate its potential

for structural optimisation.

Gain a better understanding of the kinetics of the austenite formation in boron steels, and

evaluate the influence of heating rate and soaking temperature on the progress. Based on

these, develop a set of unified equations which can effectively describe the austenite

formation in boron steel, under both non-isothermal and isothermal conditions, within or

above intercritical temperatures, for hot stamping processes.

Characterise the effects of temperature and strain rate on deformation of boron steel in a

state corresponding to hot stamping after selective heating, and develop unified

constitutive models for both the austenite and initial phase (ferrite and pearlite) of boron

steel under hot stamping conditions.

9

Characterise stress-strain relationships for boron steel having various microstructures

under various strain rates at room temperature, so as to develop a unified constitutive

model which is capable of predicting the mechanical response of press-hardened boron

steel parts with graded microstructures being subjected to crash situations in automobiles.

10

CHAPTER 2 HOT STAMPING TECHNOLOGIES AND

DEVELOPMENT

2.1 Introduction to hot stamping

Hot forming and hardening of steel is not a new invention. The technology was used in China

from the Tang Dynasty (618-907) for producing swords [47]. A skilled smith was able to create

complex forms and also harden the detail in water or oil [48]. The hot stamping and cold die

quenching process (termed hot stamping for short or press hardening) was invented and

industrialised 40 years ago in Sweden [49]. It was patented in 1974 by a local Swedish steel

works, Norrbottens Järnverk AB (NJA) which later merged into the Swedish Steel AB (SSAB),

to manufacture products with high strength and wear resistance, such as shovel blades, cutting

knifes for lawn-mowers, cutting discs for stone cutting, etc. [48, 49] This technology has been

verified and further developed at Luleå University of Technology from 1975, with their first

research project calibrated with NJA and Volvo Truck. The first press hardened component on

automobiles were intrusion door beams with reduced gauge and ultra-high strength, adopted by

Saab Automobile AB for their year model Saab 9000 in 1984 [48]. In the next three decades, due

to the advantages in meeting light weight and safety requirements, the press hardening

technology has experienced tremendous development in global in automotive applications [19,

29, 50, 51], as described in chapter 1.

Conventional hot stamping processes can be classified into two main variants: direct and indirect

[19, 52]. Figure 2.1 schematically presents the production lines of the two hot stamping methods.

In direct hot stamping, the main method being used, as-delivered hardenable boron steel blanks

cut from a coil are heated over austenitization temperature in a furnace, and subsequently

11

transferred to a press by an automated system, stamped and simultaneously quenched in closed

cold dies. Taken out from the press, the as-formed parts are usually trimmed to obtain the net

shape. In the indirect method, blanks are firstly cold preformed near to their final shapes; then,

the preformed parts are heat treated for austenitization, followed by calibration and quenching in

the pressing operation. The additional forming step in this method is to extend the forming limits

for highly complex components which are not achievable through direct hot stamping processes

[52, 53].

Figure 2.1 Hot stamping processes: (a) direct method (b) indirect method [53]

2.1.1 Boron steel – 22MnB5

Material information

The most commonly used steel grade in hot stamping processes is 22MnB5 boron steel [29],

which is widely produced by various steel suppliers, such as ArcelorMittal, ThyssenKrupp,

SSAB, etc., under different commercial names. Although the 22MnB5 steel grade is not

standardised [54], targeting the same material properties for hot stamping and applications, steel

12

products from different suppliers have similar chemical compositions. Representative data on the

composition ranges of alloys in the boron steel, provided by SSAB for Docol 22MnB5, are given

in Table 2.1.

Table 2.1 Chemical composition of a typical 22MnB5 boron steel (mass in % min-max) [55]

C Si Mn P S Cr B

0.20–0.25 0.20–0.35 1.00–1.30 0.030 0.010 0.14–0.26 0.0015–0.005

As delivered boron steel, with microstructure of ferrite and pearlite, has relatively low strength

and high ductility; the boron steel after press hardening, with microstructure of full martensite,

has ultra-high strength and reduced ductility. Data on the mechanical properties of boron steel

22MnB5 provided by different suppliers are slightly different, probably caused by the variations

in chemical compositions or testing methods. A set of data on the property ranges of 22MnB5

under different conditions is summarised and listed in Table 2.2.

Table 2.2 Mechanical properties of 22MnB5 boron steels [20, 21, 54, 55]

Condition Yield strength

(MPa)

Tensile strength

(MPa)

Elongation

(%)

As-delivered 320-550 500-700 10-26

Annealed 310-400 480-560 20-28

Hardened in water 1000-1100 1500-1650 5-7

13

Coating

Boron steel blanks are generally pre-coated with a protective layer, so as to reduce surface

oxidation and decarburization. The most widespread protection on the 22MnB5 boron steel is Al-

Si based coating which is transformed into a Fe-Al-Si layer during heating, preventing the

formation of scales. The hot-dip aluminized blanks are not applicable for indirect hot stamping

processes, which is due to the lower ductility of the Al-Si layer compared to the boron steel at

room temperature [19, 29].

Thermal-mechanical properties

Under hot stamping conditions, the influence of rolling direction and defining anisotropy, which

are usually important parameters in cold forming, are diminished, while the effects of

temperature and strain rate play a prominent role [16, 56]. Thus, investigation on the thermo-

mechanical properties of austenitic boron steel are mainly focused on the characterisation of its

viscoplastic behaviour in dependence of temperature and strain rate [23, 52, 57, 58]. Figure 2.2

and Figure 2.3 present typical stress-strain curves (symbols) of austenitic boron steel varying

with test conditions. It can be clearly seen that the flow stress level increases with decreasing

deformation temperature and increasing strain rate.

Extensive studies on materials modelling of the thermo-mechanical hot stamping process have

been carried out [25, 59, 60]. Various semi-empirical and physically based material models have

been proposed to describe the flow stress of boron steel during forming, which has been reviewed

by Karbasian et al. [29]. Figure 2.2 shows that good numerical predictions have been achieved

through Molinari-Ravichandran model and Voce-Kocks model adopted by Naderi et al. [22].

Voce-Kocks model has produced slightly better results in this figure, but Molinari-Ravichandran

is more robust because of its capacity to reproduce history effects, through the evolution law of

internal parameters [22, 29]. However, both models have described only part of the stress-strain

14

curves up to stress saturation. A set of viscoplastic-damage constitutive model based on Lin’s

modelling theories [61-63] has been adopted by Cai [16] who worked on boron steel prior to the

author’s work in the same research group. Figure 2.3 shows the whole stress-strain curves of

boron steel USIBOR 1500P provided by ArcelorMittal, where the reduction in stress due to

damage until material failure can be predicted through the material model. Thus the feature that

the material exhibits different levels of ductility at different testing conditions can be well

described. These achievements have shown that the modelling of deformation behaviour of

austenitic boron steel under hot stamping conditions is realistic.

Figure 2.2 Experimental data and numerical predictions of 22MnB5 flow behaviours at different

temperatures from 923K to 1173K at the strain rate of (a) 0.1/s and (b) 10/s [22]

15

Figure 2.3 Experimental (symbols) and numerical predicted (solid curves) flow behaviours of

boron steel (USIBOR 1500P, ArcelorMittal) at (a) different temperatures from 873K to 1073K

(strain rate: 0.1/s) and (b) different strain rates from 0.01/s to 10/s (deformation temperature:

973K) [16]

Phase transformation during quenching

Phase transformation from austenite to martenstie during quenching is crucial in hot stamping

processes. Press hardening cannot be a realistic technology without the development of metals

with high quenchability. Systematic research on the phase transformation mechanisms of boron

steels started from 1970’s [64]. It was found that a small amount of boron (0.002%–0.004%)

could have a significant effect on quenchability (i.e. the critical quenching rate for martensitic

transformation) of steels; in addition, a similar level of boron can confer hardenability in low

carbon steels, so as to enable high strength components to be formed [60]. Thus, realization of

desired phase transformation and hardenability by technically feasible cooling rates became

possible. The maximum hardenability of the materials is ensured by retaining the boron in

solution within the grains, without sufficient time for diffusion [65].

16

Figure 2.4 shows the continuous cooling transformation (CCT) diagram (in solid lines) of

USIBOR 1500P (a typical 22MnB5 boron steel with Al-Si coating produced by ArcelorMittal).

The minimum cooling rate required for complete martensitic transformation is 27K/s [24].

Figure 2.4 CCT diagram of a typical 22MnB5 boron steel (USIBOR 1500P, ArcelorMittal) under

the undeformed (solid lines) [24] and deformed (dashed lines) states

It has been reported that the plastic deformation of austenite can influence its decomposition in

steels. A high density of defects in strained austenite results in acceleration of diffusion-

controlled phase transformations, such as the formation of ferrite and pearlite, and prevents

martensitic transformation compared to non-deformed condition [66, 67]. This is an important

problem to be addressed in press hardening processes, since the critical cooling rate for full

martensite formation varies with the extent of pre-deformation and the requirement in quenching

the parts becomes more severe. Great attention has been given in the last few years to the effect

of plastic deformation on the phase transformations in hot stamped boron steel during cooling [34,

37, 68]. Barcellona et al. [69] and Naderi et al. [70] have drawn similar conclusions that the

imposed deformation facilitates the formation of bainite and ferrite in 22MnB5 steel and the

17

continuous cooling transformation (CCT) diagram shifts towards left and down (the trend is

illustrated in Figure 2.4). Min et al [71] have studied the mechanism of the phenomena and

concluded that: the plastic deformation increases the stored energy in austenite, so as to increase

the driving force and shorten the incubation time for diffusional phase transformations. At the

same time, Abbasi et al. [72] have investigated the effects of deformation temperature and strain

rate on austenite decomposition in boron steel and concluded that: dislocations in austenite halt

the motion of glissile interfaces for the coordinated movement of atoms, which results in the

impediment of martensitic transformation. To characterise the plastic strain effects, Cai [16] has

modelled the bainite transformation in deformed boron steel by taking dislocation density into

account, thus the influence of deformation conditions, such as temperature, strain rate and strain

level, can be rationalised as one factor in the model. The bainite transformation model can also

be extended to describe other diffusion-controlled phase transformations. Having the volume

fractions of bainite, ferrite, and pearlite quantified, the martensite fraction in as-quenched parts is

able to be predicted, for various hot stamping conditions.

2.1.2 Process parameters

Critical operations in a typical direct hot stamping process are heating blanks, and forming and

quenching the parts in cold dies. The temperature profile applied to boron steel sheet,

corresponding to the steps 2–4 in Figure 2.1 (a), is schematically presented in Figure 2.5.

Important process parameters during the industrial processing are discussed below:

18

Figure 2.5 Schematic of the typical temperature profile of blanks in hot stamping processes

To achieve desired austenitic microstructure, boron steel has to be heated above full austenite

formation temperature Ae3 (about 1103K–1123K for 22MnB5 [21, 56]) and soaked for a certain

time length. For the state of technology, blanks are usually heated in roller hearth furnaces to

1173K–1223K and soaked for 3–10 minutes [16, 56]. Due to the need for large volume, some

furnaces of the existing hot stamping lines are 40m in length, which requires much floor space

and is costly, and makes reducing heating time a most pressing demand on heating system [29].

Two main approaches to solve the problem are seeking alternative heating technologies and

improving process control of thermal conditions. The former one has been under development in

recent years, which is described in subsection 2.2.2.2. The latter one requires characterisation of

the effects of thermal conditions on austenitization in boron steel. In has been found that both the

increase in soaking temperature and the reduction in blank thickness enable a homogenous

austenitization to be achieved within shorter heat treatment time [29]. The influence of blank

thickness can be attributed to the effect of heating rate on the transformation, which means a

higher heating rate facilitates the austenite formation. To determine the optimised thermal

condition, further studies on the characterisation of austenite formation behaviour is desirable. A

review on austenitization in boron steel and discussion is given in detail in section 2.3.

19

The forming process has to be completed before the decomposition of austenite. Thereby, short

transfer time as well as a fast tool closing and forming operation, to minimise heat loss, are

preconditions for successful process control. On the other hand, the heat has to be extracted from

the as-formed part efficiently to ensure full martensitic transformation, which requires excellent

cooling capacity of the tool. To avoid possible thermal distortions, as-formed parts are usually

maintained in closed dies until the temperature down to 423K [56]. This further addresses the

importance of the ability of dies in extracting heat, since cooling time is the key to drive the

productivity of hot stamping in mass production. To shorten the cycle time, there are various

ways that efforts can be made. The most widely used approach is to improve the water cooling

efficiency through proper design of cooling duct in dies [29]. At the same time, tool steels with

improved heat conductivity can be adopted to accelerate the cooling rate [19]. In addition, design

of hydraulic presses with special cushions, which enables best possible contact between the part

and dies, can enhance the heat transfer due to high contact pressure over the part [73].

2.1.3 Advantages and limitations of conventional hot stamping processes

The advantages and current limitations of the conventional hot stamping processes are listed

below based on comprehensive literature review and understanding of the forming technology:

Advantages

1) Compared with conventional multi-stage forming processes, the hot stamping process is

more efficient as the forming and hardening are done in the same operation; in addition, the

equipment is relatively simple in both design and technology [74].

2) Forming force required for hot stamping is relatively low, only approximately 20–40 % of

that of cold forming of high strength steels [26].

20

3) Complex geometries can be formed due to the high formability of hot alloys, which can

enable the number of components necessary to form a part to be reduced [26].

4) Components are formed with high dimensional accuracy and good reproducibility; no

spring-back and thermal distortion, no additional modifications required [73].

5) Press hardened parts have ultra-high strength, which can enhance structure integrity as

safety components and reduce weight and cost due to less material input [73].

6) As-formed material properties are not dependent on forming depth, since there is no

residual strain after press hardening [27].

7) Since the hot stamping process involves with phase transformations during both heating

and cooling operations, there is great potential in technology innovation for microstructural

control.

Limitations

1) The increasing demand for a higher efficiency of forming processes inevitably leads to the

question of how to shorten the process cycle time [29], however, the productivity of hot

stamping processes is limited by the cooling time of the parts in press [73].

2) The safety component with uniformly ultra-high strength does not always well meet energy

absorption requirements.

3) Dies for cutting of the press hardened UHSS steel are expensive and have high maintenance

costs; the current solution to trimming the parts with laser is slow and also very expensive

[56].

4) Heating of blanks to high temperatures in furnaces increases the cost of hot stamping [29].

21

2.2 Tailored solutions in hot stamping

The previously mentioned limitations of a conventionally press hardened UHSS part, in crash

performance and trimming operations, can be overcome by locally introducing regions with

increased ductility and decreased strength in the part. As discussed in Chapter 1, great attention is

being paid to produce parts with tailored distributions of physical characteristics through

technology innovation in hot stamping. The solutions to this at the state of art are reviewed in this

section.

2.2.1 Manufacturing of hot stamped parts with tailored properties

2.2.1.1 Additional operations to hot stamping

To produce a part with tailored mechanical properties, in principle, effort can be made by varying

the three physical characteristics: material, thickness, and microstructure, which have all been

implemented in hot stamping processes through additional operations.

Tailored welded blanks (TWB)

Forming parts using tailored welded blanks (TWB) is wildly used in cold sheet metal forming,

but it is a recent technology for hot stamping [75]. Usually, heat-treatable and non-heat-treatable

steel steels are trimmed and laser welded together as the blank for hot stamping. The strength of

the heat-treatable steel increases due to the formation of martensite in an as-formed part, contrary

to that of the non-heat-treatable one, thus tailored properties of the part are obtained. For

example, ArcelorMittal has developed a hot stamping material, DUCTIBOR 500P, which is

designed to maintain high ductility after forming and quenching, with a UTS of 500 MPa and

elongation at fracture over 15%. Therefore, by using TWB consisting of USIBOR 1500P and

DUCTIBOR 500P in hot stamping, a part with both high strength and high ductility regions can

22

be produced [37, 39, 76, 77]. A schematic illustration of the technology applied in producing a B-

pillar is shown in Figure 2.6 (a). In addition, TWB can be a combination of sheets in different

thickness, which has also been used to produce safety critical components in cars, such as rear

side members [78]. Besides, another new technique related to TWB is called patchworks: patch

blanks are welded on top of a mother blank as local reinforcements, so as to distribute the

thickness according to the structural requirement [76]. This concept has been implemented on

mass production of B-pillar by Benteler, by using USIBOR 1500P 2mm thick blank as master

part and 1mm thick blank as the patch [79].

It has to be noted that the welded seam in TWB has limited formability, which decreases the

complexity of shapes achievable. At the same time, since any surface coating has to be removed

before welding, oxidation around welding areas during heating is another problem. In addition,

for TWB with varying thickness, including patchworks, the thickness discontinuity should be

allowed for in tool design.

(a) (b)

Figure 2.6 Schematics illustrating the manufacturing of hot stamped B-pillars from (a) tailored

welded blanks (TWB) [29, 75], and (b) tailored rolled blanks (TRB) [80, 81]

23

Tailored rolled blanks (TRB)

Tailored rolled blanks (TRB) are made of the same material with variable thickness profiles by

rolling processes within the same blank [75, 79]. Due to the potential in reducing weight and

locally adjusting part behaviour [79], TRB has been applied in hot stamping for automotive

applications since 2006 and the TRB hot stamped parts have been used in at least 12 recent

automobiles, including Ford focus, VW Gofl, BMW 3/X5/X6, and Audi A3 [82]. The technology

applied in producing a B-pillar is schematically shown in Figure 2.6 (b).

Compared with TWB, more precise tuning of the shape can be achieved by TRB due to the

possibility to get many stepped changes in the thickness of the part, with a smooth transition at

each change instead of weld seams. But, again, the variation in blank thickness is a concern in

tool design, since the precision of the formed shape and good contact between the blank and dies

for complete martensite transformation are required. In addition, the cost for TRB is adversely

affected by a potentially lower material utilisation ratio due to nesting constraints in the strip [76].

Post tempering

The application of this technology in hot stamping is concerned with a tempering treatment

conducted on portions of a fully press hardened part, in order to locally change the martensite to

ductile phases with lower strength [76]. It has also been applied in producing automotive safety

critical part, such as rear side members [83]. Compared with TWB and TRB solutions, post

tempering is more locally adjustable in tuning the properties, capable of taking care of small

features. But it can take as long as several minutes to treat a part [37].

In addition to the shortcomings previously discussed for each solution, the common downfall for

all of them is the addition of another operation (welding, rolling, and tempering) in the

24

production chain, which increases the cost and weakens the advantage of hot stamping for being

capable of producing products within one operation.

2.2.1.2 Selective heat treatment strategies integrated in hot stamping

Due to the intrinsic advantage of hot stamping for its potential in microstructural control, new

strategies, to obtain a tailored part from a single blank through tailored process control in a single

hot stamping operation, are more promising solutions compared with the ones discussed in the

previous subsection. Two main strategies, to control phase transformation in boron steel by

selective heating or cooling, are introduced below:

25

Figure 2.7 hot stamping of a B-Pillar with graded microstructures by selective heat treatment: (a)

Image of a hot stamped B-pillar being partially hardened [40], with a temperature profile of a

selective cooling process in a continuous cooling transformation (CCT) diagram (b) An as-

formed B-pillar with graded properties, and the typical tensile properties of the martensite and

initial phase of boron steel (c) Image of a blank being partially austenitized, with a temperature

profile of a selective heating process in a continuous heating transformation (CHT) diagram

26

Selective cooling for partial press hardening

In this concept, the whole boron steel blank is fully austenitized but only a part of it is quenched

to martensite during cooling. The mechanism of the strategy is illustrated through an example of

the production of a tailored B-pillar in Figures 2.7 (a) and (b). Figure 2.7 (b) shows the different

regions in the B-pillar desiring different mechanical properties: ① is a hard zone with martensite

to provide high intrusion resistance, ③ is a soft zone with ferrite and pearlite phases for high

energy absorption, and ② is the transition zone where the mechanical properties vary with the

microstructural phase compositions. To achieve this, in Figure 2.7 (a), thermal conditions for the

hot stamped B-pillar in dies are controlled to enable a high cooling rate in zone ① for martensite

transformation and a low cooling rate in zone ③ for ferrite and pearlite transformation. With

respect to the transition zone, a representative cooling curve ② is presented in the continuous

cooling transformation (CCT) diagram of boron steel in Figure 2.7 (a), where multiple phase

states can be obtained. The length and microstructural distribution of the transition zone are

determined by applied cooling rate gradient. The process control of cooling conditions can be

realised in various ways. For example, ‘tailored tempering’ is currently a popular technology

patented by ThyssenKrupp: by partially heating the stamping dies, the temperature difference

between the hot blank and the stamping die in the heated zones is lower, thus the blank cools

more slowly in these areas [40]. A detailed review about the implementation of the selective

cooling strategy is given in subsection 2.2.2.1.

Selective heating and press hardening

In this concept, only a part of the boron steel blank is austenitized for subsequent hardening,

whereas the other part remains the initial phase state throughout the hot stamping process. To

match the discussion about selective cooling, the mechanism of the selective heating strategy is

also illustrated in Figure 2.7, taking the production of the same B-pillar as an example. Figure 2.7

27

(c) shows the selectively heated blank before forming, as well as different temperature profiles

applied on the different regions of the blank. In the continuous heating transformation (CHT)

diagram of boron steel, there are three regions of phase states: full austenite, partial austenite

combined with partial untransformed phase, initial phase. Hard zone ① desiring full martensite is

heated and soaked to the full austenite region (about 1173K) in the CHT diagram, and soft zone

③ is heated to medium temperature (about 973K) to retain the initial phase of boron steel (ferrite

and pearlite). The transition zone ② soaked at the intercritical temperature region is partially

austenitized. Provided the quenching is sufficient, the portion of austenite in the hot blank

determines the portion of martensite in the press hardened B-pillar part. The length and

microstructural distribution of the transition zone in the final part depend on the applied

temperature gradient on the hot blank. It is noted that, different from the transition zone produced

by selective cooling which can consist a large fraction of bainite, the transition zone produced by

selective heating is mainly composed of the austenite and initial (ferrite and pearlite) phases, the

mechanisms of which is illustrated by the CCT and CHT diagrams in Figure 2.7. The approaches

to realise the selective heating control are discussed in subsection 2.2.2.2.

2.2.2 Technologies for process control of thermal conditions

2.2.2.1 Selective cooling solutions

The key mechanism for achieving desired cooling rates within selected regions of the dies and

the part therein is heat transfer control. The concepts introduced in subsection 2.1.2 for

improving the quenching efficiency can be implemented adversely to obtain a lower cooling rate.

All approaches available in literature can be summarised as the control of temperature difference

and heat transfer coefficient (HTC) between the blank and dies [45, 84]. Specific technologies

are introduced below:

28

Differential die temperatures

The cooling rate of a part can be reduced by increasing the temperature of the die. Heat transfer

between the blank and dies will decrease due to a lower temperature difference. Therefore, by

heating or cooling different tool zones to different temperatures, the properties of the produced

part can be selectively adjusted in terms of graded microstructure. HONDA MOTOR has

proposed this concept in a patent for microstructural optimisation of automotive structures [85].

The implementation of the concept by ThyssenKrupp, as introduced in subsection 2.2.1.2, is

currently being tested under production conditions [40]. Extensive studies on the efficient control

of this process have also been conducted [34, 38, 86].

Differential die surfaces

The cooling rate of a part can be affected by the contact conditions with dies. Since boron steel is

not hardened by air cooling, the strength distribution in the part can be controlled by limiting the

contact with dies to certain portions [18]. A problem for the design of partial contact gaps is that

the shape accuracy of the part corresponding to the gap areas cannot be guaranteed. A solution to

the problem is to make textures on die surfaces, so that the heat transfer coefficient (HTC) is

reduced due to the clearance between the blank and dies [23, 87]. Figure 2.8 schematically shows

the different types of tool surface textures, which has been patented by Gestamp Hardtech [87].

Figure 2.8 Textures on die surfaces [87]

29

Differential thermal conductivities

Selective cooling of a part can be achieved by having tools with varying thermal conductivities.

For example, Steatite plates, with very low thermal conductivity, were embedded in the blank

holder and die by Mori et al. [18] to prevent hardening of the flanges of a part. The recently

developed nanocasting technology enables tools with complex cooling strategies to be realised at

a reasonable cost and any desired conductivity variations ranging from 7 to 66 W/m·K [19].

Differential applied pressures [34]

Since HTC is a function of pressure between the contacted surfaces, heat transfer between the

blank and dies can be controlled by applied contact pressure. Selective cooling of a part can thus

be realised by applying differential pressures through special tool design and process control.

This concept has been studied by Merklein et al. under laboratory conditions [34].

2.2.2.2 Advanced techniques for selective heating

Different from the selective cooling solutions which have been well developed, the development

of technologies in heating for tailored solutions are still at the preliminary stage. Novel attempts

and potentials in implementing the selective heating concept into different types of heating

systems are reviewed and discussed below:

Furnace - radiation and convection heating

On conventional hot stamping production lines, blanks are heated by radiation and convective

flow of heat in continuous furnaces [29, 88]. For blanks with certain properties and thickness, the

heating rate is determined by the speed of transport (by rollers or walking beams) and the

temperatures in different consecutive chambers [88]. Tailored solutions can be realised in

30

furnaces, for example, by partially shielding the blank from thermal radiation, or setting selective

heating zones which are isolated from each other by a wall [76].

Resistance heating

In resistance heating, the heated part is connected in series with a power source. The electric

resistance of metal part causes the heating of itself. The heat generated is proportional to the loss

of power. For a higher efficiency factor, the resistance heating is mainly used for long

components, such as pipes, rods, wire and bands. The problem limiting its industrial application

is the difficulty in getting homogeneous heating temperature fields over the components [29].

Nevertheless, this technology has its potential in sheet metal forming for specific selective

heating. Mori has conducted extensive studies on the resistance heating for a few years [18, 35,

89, 90], and developed a selective heating technique called ‘bypass resistance heating’. Figure

2.9 shows the principle of the heating technique. In the heating system, the zone in contact with

the copper bypasses has a large cross-sectional area and low resistance. Due to the passage of the

current though the copper bypasses, the zone is not heated. Thus, specific portions desiring low

strength can be targeted through the bypass resistance heating. In addition, the power loss by

adopting bypasses is minor because the copper bypasses are thick and short [35]. This technique

is currently at a laboratory level.

Figure 2.9 Principle of selective heating of a steel sheet using bypass resistance heating [35]

31

Induction heating

When an electrical-conducting metal component enters the inductor of induction heating system,

the electric current is induced in the component and consequently heat is generated [19].

Induction heating can provide very high energy supply rates and thus meets industrial

requirements for mass production [91]. It is currently at the stage from laboratory investigation to

industrial applications in hot stamping, which would be a promising alternative heating

technology due to its ability to significantly reduce the heating time, resulting in lower

investment costs and reduced floor space for the heating device [88, 92]. The combination of

induction heating with other heating techniques can be used to realise selective heating of boron

steel blanks. Maikranz-Valentin et al. [5] have produced tailored components by uniformly

heating 22MnB5 boron steel blanks to medium temperatures without phase transformation in a

furnace, and partially re-heating above Ac3 in intended high strength areas by using induction

heating. Ploshikhin te al. [91] has proposed a contact heating technique called ‘contact heat

treatment’, for the application in preconditioning of boron steel blanks for press hardening. In

this technique, the induction heating is employed to supply energy to two contact plates, and the

contact plates are used to heat the boron steel blank through conductive heat transfer, as shown in

Figure 2.10. By making blanks partially contact the hot heating plates, or changing the contact

conditions for varying heat transfer coefficient between blanks and heating plates, differential

temperature regions can be obtained, so as to create parts with desired tailored properties.

Figure 2.10 Principle of contact heating [91]

32

2.2.3 Analysis of the selective heating and press hardening strategy

Based on the above review and discussion, it can be appreciated that the tailored solutions for

structural optimisation through selective heat treatment are advantageous and achievable for

industrial applications. Compared with selective cooling, the selective heating and press

hardening strategy lacks development. The possible reasons might be: the fundamental

understanding of boron steel decomposition (subsection 2.1.1) and practical implementations for

cooling process control have drawn great attention since the development of conventional hot

stamping processes, for the purpose of efficient martensite transformation. The knowledge and

techniques can be directly used or adapted to selective cooling solutions. By contrast, the

selective heating and press hardening process involves intercritical annealing of boron steel and

deformation of boron steel in multiple phase states, with which the conventional hot stamping

process is not concerned. As a result, there are gaps existing in the relevant knowledge base.

However, attention to the selective heating and press hardening strategy is encouraged. The

significant and unique advantages of the new strategy are discussed below:

1) Compared with selective cooling, the most critical advantage of selective heating is the ability

to shorten process cycle time. The demand for short cooling time to improve manufacturing

efficiency and the requirement for slow cooling rate to ensure ductile phase transformation is the

intrinsic contradiction and vital drawback of selective cooling solutions. The proposed process,

during which the blank is fully quenched, can avoid that problem; at the same time, lower heat

(due to lower temperatures in partial regions) in the blank to extract can facilitate the cooling

efficiency further.

2) Compared with selective cooling solutions which are all associated with design of tool features

(e.g. tool cooling and heating tunnels, tool surfaces and materials, etc.), the selective heating

strategy can directly be applied using the conventional hot stamping tool, and it has the flexibility

33

in tuning microstructural distributions in a part for optimised structural properties without

remaking or modifying the tool.

3) By applying selective heating and press hardening strategy, development of advanced heating

technologies will be stimulated; at the same time, lower heat is required by the partial heated

blank. Thus improvement in energy efficiency is possible.

Thereby, it can be concluded that the selective heating and press hardening strategy is a

promising forming technology, which has the potential in substituting selective cooling solutions,

or as least expand the applicable range of hot stamping, for tailored components. Whereas, for

the new forming process, concerns exist about formability and possible spring-back of the

partially austenitized boron steel blank [29]. Nevertheless, no proof for the problems or

assessment of the strategy was found in current literature. Therefore, a feasibility study on this

strategy is necessary. At the same, fundamental studies of the thermo-mechanical behaviour of

boron steel in the initial phase state under hot forming conditions are also needed.

Provided the feasibility of the selective heating and press hardening strategy is validated, its

potential can only be maximised by optimising the structural performance of a part through

effective process control. This is concerned with grading the microstructural distribution

(including martensite zone, multiphase zone, and ferrite and pearlite zone) in a part by

controlling the austenitization process during selective heating, which can only be realised when

the relationship between mechanical properties of as-formed boron steels and the corresponding

microstructures achieved by certain thermal conditions is quantitatively determined. Therefore,

understanding and modelling the formation of austenite in boron steel under selective heating

conditions, as well as the mechanical response of boron steel with various microstructures in a

collision situation are critical. The studies on the two aspects in current literature are reviewed in

the next two sections.

34

2.3 Microstructural control during heating

In the selective heating and press hardening process, the transformation of austenite during

heating is of primary importance in deciding the final properties for a given part. Therefore,

understanding and modelling the kinetics of austenite formation have great significance in

optimising the design of heat treatment conditions.

2.3.1 Studies on austenite formation

Studies on austenite formation in steels have been carried out by many researchers [43]. Robert

and Mehl established the nucleation and growth character of the transformation in steels with

different starting microstructures [43, 93, 94]. However, compared with the number of

investigations into decomposition of austenite during cooling, studies on austenite formation

have been few [43, 44, 93, 95-97]. This is primarily because it is difficult to retain austenite at

room temperature for inspection and characterisation, which makes observation of the progress of

austenite formation difficult [43, 95, 97].

Stimulated by automotive applications, the development of advanced high strength steels has

recently revived interest in the heating stage of the heat treatment cycle [93, 98-101]. Initially,

attention was focused on partial austenite formation in intercritical annealing practices, since this

offers a means of optimising the mechanical properties of dual-phase steels [42, 97, 99, 102-104].

More extensive and systematic research on the formation of austenite has been conducted during

the last decade, in order to achieve quantitative understanding of microstructural evolution during

transformation and the mechanisms that control it under different conditions [41-43, 95, 103-111].

However, the influence of temperature and heating rate on the progress of the transformation to

austenite has always been studied separately under isothermal conditions [42, 103-105, 112] and

non-isothermal conditions [16, 101, 106, 107, 113], respectively. In a real situation, the

35

conditions for work-piece preheating for hot pressing are first increasing temperature followed by

steady-state temperature. This should be recognised if an accurate evaluation of austenite

evolution is to be obtained.

Information on austenite formation in boron steels for hot stamping applications is sparse. Cai et

al. [16, 114] have carried out some relevant research but it focused on only full austenite

formation required by conventional hot stamping processes. Little research has been carried out

on the intercritical soaking of boron steels.

2.3.2 Modelling of austenite formation

Based on the efforts in the last decades, there are various types of austenitization models having

been developed. According to calculation methods, they can be generally classified as

probabilistic models and deterministic models [109]. The former type introduces stochastic

variables into calculation process, which can account for the stochastic character of the phase

transformation and give qualitative representation of the microstructure [42, 109, 113]; the latter

type is based on the time-integration of equations consisting of certain state variables, so as to

characterise the microstructural evolution, in various length scales depending on the features of

interest, throughout the phase transformation. The deterministic models have been predominant

for describing the austenite formation in literatures. The main development methods are

analytical approaches and phenomenological approaches [43].

Analytical approaches are mainly based on the analysis of mechanisms which control the

austenite front migration, which requires assumptions (e.g. on growth modes) being strictly

defined in advance. However, it may not be easy when the phase transformation mode is of a

complex character [43, 94, 95, 101, 103, 109, 115, 116]. For austenitization in a manganese-

boron steel with the ferritic-pearlitic starting microstructure, depending on heating conditions, the

36

growth of austenite phase can be controlled by interface reaction or volume diffusion[95], and the

latter one could be carbon diffusion in austenite or manganese diffusion in ferrite [43, 117]. In

this case, the analytical approach may not be an efficient way to adopt in this study.

Phenomenological approaches are mainly conducted by relating the transformation progress to

the change of austenite volume fraction with time. The Avrami’s equation plays an critical role in

the fundamental understanding of the transformation [118]. But it is too simple to adapt to any

specific case, e.g. a transformation has mixed nucleation or alternate growth mode. Thereby

extensive studies have been conducted to further develop of the equation, so as to fit it to

different transformation conditions [42, 96, 101, 106, 113, 119]. However, same as the problem

pointed out in the previous subsection, it is found that the transformations of austenite under

isothermal and non-isothermal conditions have been always modelled separately. Thus possible

influence of heating rate on the subsequent isothermal transformation cannot be accounted for.

Efforts for adapting the modelling knowledge to the austenite formation in boron steel have been

few. An attempt has been conducted by Cai [16] by developing a set of unified equations with an

incubation factor and austenite volume fraction as state variables, taking the heating rate into

account. However, this model is applicable to only continuous heating conditions. For the hot

stamping practice, the boron steel is treated with continuous heating followed by steady soaking;

in addition, intercritical annealing for partial austenitization is involved under selective heating

conditions. Therefore, an austenite formation model which can be applied to the complex heating

conditions is highly demanded.

2.4 Final properties of hot stamped panels

One precondition to introduce tailored parts in automobiles is the development of predictive

models for crashworthiness analysis, which requires the identification of the mechanical

37

characteristics of as-formed boron steels with various microstructures, under a wide range of

strain rates. Therefore, a study on the final properties of hot stamped boron steels is critical to the

implementation of the selective heating and press hardening strategy.

The mechanical properties of martensitic boron steel, achieved through conventional press

hardening processes, are well known and usually provided as product information by steel

suppliers (given in Table 2.2 in subsection 2.1.1). Relevant studies are not many, mainly about

fracture analysis [120], cooling rate effects [45], and strain rate effects [121] on the mechanical

response of boron steel with full martensite.

Only due to the popularity of tailored concept, interests in hot stamped boron steels have been

stimulated in the very recent years. But the information is still scattered in current literature. The

most intensive research has been conducted by Bardelcik et al. [36, 37, 45, 122, 123] in the

University of Waterloo. In their work, the approach to achieve tailored parts was based on the

selective cooling concept. A variety of as-quenched material conditions were produced for tensile

testing with various strain rates, hardness testing, and microstructural analysis. A set of

representative test results are given in Figure 2.11 [37]. ‘FAQA’ and ‘Quench/Def.’ were two

types of as-quenched boron steel samples obtained through different process control. ‘FAQA’

was composed of only martensite and bainite; ‘Quench/Def.’ was composed of martensite,

bainite, and ferrite, with the ferrite fraction in each sample measured and shown in the figures. It

was found that, due to the presence of ferrite, there was little change in material strength, but a

dramatic increase in the uniform elongation for a given hardness level less than about 350 HV. It

indicates that more fractions of ferrite would benefit the energy absorption of a hot stamped part

with graded microstructures. In addition, as can be seen in Figure 2.11 (b), the lowest value of

uniform elongation didn’t correspond to the highest hardness value, but some point between

38

350HV and 450 HV, which suggests the multiphase boron steel with a certain phase composition

may have the worst ductility.

Figure 2.11 (a) Ultimate tensile strength (σUTS

) and 0.2% yield stress (σ0.2%

) and (b) Uniform

elongation versus Vickers hardness from the quasi-static tension tests conducted at a strain rate of

0.003 /s (The error bars represent +/- the standard deviation of repeated test results) [37]

Bardelcik et al. have also developed several constitutive models to enable a part with graded

microstructures, produced by selective cooling, to be simulated in a crash situation [36, 37, 122].

The most advanced one, termed ‘Tailored Crash Model II’, is given below:

( / ([ ], ))

( , ,[ ], ) ([ ], ) ([ ], ) ([ ], ) 1

MC F D

M BM M M M

f F A F B F A F eM B M B M B M B

(2.1)

where D is a constant, parameters A, B, and C are functions of martensite-bainite fraction

relationship [M/(M+B)] and ferrite fraction F. The model is based on the Voce hardening law

with exponential-type strain rate sensitivity, capable of describing the strain rate effects, strain

hardening response and overall energy absorption behaviour of a part with varying volume

fractions of martensite, bainite and ferrite.

39

The above mentioned work is an appreciable research effort. However, the investigation was

conducted on boron steel obtained from selective cooling processes, with bainite, instead of

ferrite, as the dominant soft phase. For multiphase boron steel achieved from selective heating

processes, with ferrite as the dominant soft phase, the previous results and deformation

mechanisms may not be applicable. In addition, an accurate prediction of material failure is

critical for crashworthiness simulation. But the ‘Tailored Crash Model II’ is not capable of

capturing the damage characteristic of material. Consequently, the important feature of reduced

ductility for multiphase boron steel with certain phase compositions, shown in Figure 2.11 (b),

cannot be described. It is critical to characterise the ductility of boron steel in various phase

compositions, so as to avoid unexpected failure at transition zones. Therefore, the development

of a more functional constitutive model is demanded.

Studies on the final properties of boron steels produced from selective heating and press

hardening processes are much fewer and preliminary. Li et al. [124] and He et al. [46] both tested

the hardness and quasi-static tensile properties of boron steel samples, which were heated to

different soaking temperatures and fully quenched. However, in their studies, the mechanical

properties were related to only soaking temperatures and no microstructural analysis was

conducted. Thus, a further study to quantitatively determine the relationship between the

microstructural and mechanical characteristics of boron steel is desired. In addition, the

characterisation of the strain rate sensitivity of boron steel with ferrite and pearlite phases has

never been done in literature, but it is necessary for the calibration of appropriate constitutive

models.

2.5 Summary

Conventional hot stamping processes, advanced technologies in hot stamping of tailored parts, as

well as the associated studies on boron steel properties have been comprehensively reviewed. It

40

is found that the selective heating and press hardening strategy can well extend the limitations of

the conventional hot stamping technology and selective cooling solutions, but there are large

gaps in the relevant knowledge basis for the development of this technology. By identifying the

research deficit in literature, the necessity of the fundamental studies, on the austenite

transformation and deformation behaviour of boron steel under selective heating and press

hardening conditions, as well as on the mechanical properties of press hardened boron steel with

various microstructures, has been addressed.

41

CHAPTER 3 FEASIBILITY STUDIES FOR THE

SELECTIVE HEATING AND PRESS HARDENING

STRATEGY

3.1 Introduction

In this chapter, feasibility studies for the proposed strategy, termed as selective heating and press

hardening, carried out through a set of specially designed experimental programme are described.

The objectives were validation of the strategy and demonstration of its potential for structural

optimisation. In the work, a lab-scale demonstrator part was designed and relevant manufacturing

and property-assessment processes were defined. A heating technique and selective-heating rigs

were designed to enable certain microstructural distributions in blanks to be obtained. A hot

stamping tool set was designed for forming and quenching the parts. Test pieces were formed

under various heating conditions to obtain demonstrator parts having variously graded

microstructures. Microstructural distributions in the as-formed parts were determined through

hardness testing and microstructural observation. Ultimately, structural performance of the parts

was evaluated through bending tests.

3.2 Experimental design

3.2.1 Concept illustration

The concept in the study is the optimisation of structural performance of press-hardened parts by

means of microstructural design, realised by controlling thermal conditions during preheating in

hot stamping processes. Figure 3.1 schematically shows in simplified form, the disposition of

42

microstructure in work-piece and formed part and the method of assessing mechanical properties.

Figure 3 (a) illustrates a portion S/L of a work-piece, the hot zone, fully austenitized by heating

to and soaking at a temperature of 1173K. The two ends, the warm zones, are heated to a

temperature below austenitization start temperature, 993K [21]. Thereby a warm zone is

composed of the initial phase, and multiphase in the transition regions adjacent to the hot zone.

Figure 3 (b) shows the pressed shape, representing an impact beam, which has been die quenched

and is fully martensitic in the prior hot zone. Figure 3 (c) shows load bearing assessment of the

as-formed part through three point bending test. The performance of the part would vary with the

length of full martensite zone (hard zone) and this can be optimised in the selective heating

operation to comply with a particular design specification.

Figure 3.1 Schematics illustrating the manufacturing process and experimentation for function

assessment (a) Selective heating of the work-piece (b) An as-formed part after hot stamping and

cold die quenching (c) Three point bending of the as-formed part

43

3.2.2 Material and demonstrator part

The material used in this study was a 22MnB5 manganese-boron steel provided by the project

sponsor SAIC MOTOR. It was cold rolled and hot-dip aluminized. Product information provided

by steel supplier: the initial microstructure contained about 78/22 mixture of proeutectoid ferrite

and pearlite; the chemical composition of the investigated steel is listed in Table 3.1. All work-

pieces used for the experiment were machined from the same batch of as-delivered, 1.6mm thick,

boron steel sheet.

Table 3.1 Chemical composition (Max value - ladle analysis in %) [21]

C Si Mn P S Cr + Mo Ti B

0.25 0.40 1.40 0.025 0.010 0.50 0.05 0.005

Figure 3.2 shows the cross-section of a lab-scale demonstrator part, the length (L) of which was

320 mm. The dimensions of the initial blank were 80mm × 320mm.

Figure 3.2 Cross-section of a demonstrator beam (dimensions are in mm)

3.2.3 Test programme

By taking the length of hot zone, S, as a variable, four test conditions were defined and they are

listed in Table 3.1, where S-60mm and S-100mm are two conditions designed for selective

heating with 60mm and 100mm hot zones respectively, and S-0mm and S-320mm represent

44

uniform heating without a hot zone and with full hot zone respectively. In addition, assessment of

both microstructural and structural properties of as-formed parts was conducted for conditions

presented in Table 3.2.

Table 3.2 Test programme (‘√’ represents the selected test conditions)

Test

condition

Hot

forming

Hardness distribution Microstructure

observation

Bending

tests Sectional Longitudinal

S-0mm √ √

S-60mm √ √ √

S-100mm √ √ √ √

S-320mm √ √ √

3.3 Heating technique

Selective heating is an essential part of the strategy. In this work, it was realised by local contact

heat treatment in a furnace under laboratory conditions. The implementation is shown in Figures

3.3 (a) and (b). A selective heating rig, consisting of two heating blocks made of stainless steel,

served as an energy reservoir for locally heating a blank in a hot zone. It was prepositioned in a

furnace and preheated to a temperature above 1173K. Heat transfer in the hot zone took place

when a cold work-piece was positioned between two hot blocks. At the same time, the two ends

of the work-piece, the warm zones, mainly heated by radiation and convection within the furnace

were thus heated at a lower rate and their maximum temperature was controlled to just below

993K.

45

Figure 3.3 Selective heating technique (a) Set-up of facilities for selective heating and

temperature measurement (b) 3-D diagram of the selective heating rig (c) Location of

thermocouples attached to a work-piece (dimensions in the figure are in mm)

With respect to the selective heating rig, in Figures 3.3 (b), the blocks were massive to ensure

sufficient heat capacity. In addition, the top block was designed to be larger to provide higher

pressure between work-piece and blocks and enhance heat transfer. Ceramic plates were inserted

between the blocks to give them 1mm gap during preheating, in order to enable easy separation

before positioning the work-piece. Two pairs of hot blocks were made for 60mm and 100mm of

hot zones. To enable the two selective heating conditions, S-60mm and S-100mm, to share a

unified process control, the heating rig should be of the same heat capacity for both conditions.

Since hot blocks for S-100s were wider, an additional block was placed beneath the selective

heating rig for the S-60mm condition, so that the total volume of the heating blocks was the same

as that for the S-100mm heating blocks.

46

The effective control of thermal conditions to ensure a desired temperature distribution in a

work-piece was required. Therefore, thermocouples were attached to a work-piece to monitor

temperature profiles and enabled a suitable heating procedure to be determined. Figure 3.3 (c)

shows the location of thermocouples on the work-piece. In order to avoid possible influence on

the contact between the work-piece and blocks, small holes were drilled perpendicular to

through-thickness section to fix K-type thermocouples of 0.5mm in diameter. The output ends of

the thermocouples were connected to a National Instruments data logger for data acquisition, as

shown in Figure 3.3 (c).

For selective heating conditions, since the preheated rig was a massive heat resource in the small

chamber, the reduction of environmental temperatures had to be realised by opening the chamber

at intervals, to enhance air convection. The temperature profiles were decided by preheating

temperature of the hot blocks and the time to increase and reduce air convection. Trial and error

was adopted, aiming to get full austenitization in the hot zone with no phase transformation in the

warm zones. The determined thermal parameters and operation procedure for the selective

heating, which were used as standards for all following hot stamping tests, were given as follows:

1) The selective heating rig was preheated to 1253K in the furnace;

2) The furnace control temperature was set to 943K right before positioning the work-piece;

3) The work-piece was positioned between hot blocks, and the furnace door was kept open for air

convection for 140 seconds;

4) The furnace door was closed for no external air convection for 80 seconds;

5) External air convection was initiated for 60 seconds;

6) External air convention was prevented for 90 seconds;

7) External air convection was initiated for 30 seconds;

8) External air convection was prevented for 100 seconds.

47

9) The work-piece was removed from the furnace.

Figures 3.4 (a) and (b) respectively show the obtained temperature profiles of different positions

of the work-piece under S-60mm and S-100mm conditions. For each condition, temperature

gradients along the work-piece can be seen. The adjustment of air convection is revealed by the

sawtooth-shape of temperature profiles for warm zones (i.e. thermocouples B, C, and D) in both

figures. The amplitude of these temperature vibrations can be reduced by increasing the

frequency and decreasing the time intervals of air convection. However, the feasibility of manual

controlling the procedure limited the rate at which the operations could be undertaken.

For uniform heating, S-0mm and S-320mm, no hot blocks were used and the work-piece was put

into the furnace with environmental temperatures of 973K and 1173K respectively for 500

seconds.

Figure 3.5 shows the summary of final temperature profiles obtained for the four test conditions.

Representative positions are chosen, for example, ‘S-100mm-A’ represents the hot zone

temperature measured by thermocouple A for S-100mm test condition. Good consistency for S-

60mm and S-100mm was achieved. As seen in the figure, full austenitization was expected at the

hot zone for selective heating conditions, as that for the uniform heating condition S-320mm; no

phase transformation was expected at the portion D of warm zones, as that for S-0mm. In

addition, if the time of transform of work-piece from furnace to tools after soaking is known, the

natural cooling curves can be used to estimate the starting forming temperature for various

conditions.

48

(a) S-60mm

(b) S-100mm

Figure 3.4 Temperature profiles of different positions of a work-piece under selective heating

conditions: (a) S-60mm, (b) S-100mm

49

Figure 3.5 Temperature profiles for 4 different test conditions

3.4 Hot stamping

3.4.1 Design of hot stamping tool set

A hot stamping tool set was designed to be set on a hydraulic press for forming the demonstrator

part. The two main functions of the tool are to form the work-piece and extract heat from it at a

high rate [19]. For 22MnB5 manganese-boron steel, the minimum value of quenching rate

required to achieve full martensite is for the undeformed state, and is 27K/s [16]. An additional

attribute of a tool is that it should enable a part with, as near as possible, uniform thickness to be

produced. Thus, tool design has to be associated with careful consideration of both material flow

and heat transfer.

A section of the tool is presented in Figure 3.6 to schematically illustrate its working mechanism.

To well arrange the material flow, the top die was designed to be composed of two parts. The

50

main part of the top die (sides in Figure 3.6) was fixed to the ram of the press and the punch was

seated on gas springs, to allow it relative movement. Figure 3.6 (a) shows the start of forming

when the work-piece was in contact with the punch. With the whole top die set moving down, the

middle groove was formed and, as shown in Figure 3.6 (b), the punch was brought to rest by the

counterpunch while the sides continued to move downwards until the part was fully formed, as

shown in Figure 3.6 (c). Arrows in solid lines represent forming occurring under the particular

tool part. Little stretching of the blank occurred and it was subjected to near pure bending. Since

heat transfer coefficient depends on contact pressure, tight contact between work-piece and tool

is essential. In this design, see Figure 3.6 (c), the flexible top die set guaranteed tight contact over

the interfaces ①, ②, and ③. In addition, two side parts of bottom die were also adjustable,

which made sure tight contact over the interfaces ④ and ⑤. An additional feature of the tool was

that beams with different groove depths could be formed, by changing the thickness of a

replaceable block in the counterpunch.

A 3-D drawing of the assembled tool set is given in Figure 3.7. Since the tool set was for

laboratory application instead of mass production, no water cooling channels were needed in the

dies. The dies were made of AISI type H13 hot work tool steel. The die clearance was 0.1mm

(6.25%), for the work-piece in 1.6mm thickness.

51

Figure 3.6 Schematics illustrating the working mechanism of the tool set and material flow of the

work-piece (a) Start of forming (b) during forming, middle groove has been formed (c) final

stage of forming

Figure 3.7 Isometric view of the hot stamping and cold die quenching tool set

52

3.4.2 Hot stamping experiments

Hot stamping experiments were carried out on a 1000KN hydraulic testing machine. The set-up

of facilities is shown in Figure 3.8. The furnace was used for heat treatment of work-pieces

determined as described in the previous section. The controller was used to operate the machine.

A load cell was set on top of the tool set to measure the forming force. The forming speed was

150mm/s, which was determined to be appropriate to industrial processes, giving an average

strain rate of 0.5/s approximately. Forming force and punch displacement were monitored

through a digital work station, to ensure that the load provided by the machine was sufficient and

the forming speed was accurate. The time for transferring blanks to the tool set was controlled at

about 3 seconds. The times for positioning and forming were about 1 and 0.2 seconds

respectively. Formed parts were held in dies for about 20 seconds.

Figure 3.8 Set-up of facilities for hot stamping experiment

1000kN Testing Machine

Controller

Digital Work Station

Tool Set

Furnace

Load Cell

53

Figure 3.9 View of the cross-section of a formed product

Figure 3.9 shows the cross-section of a formed product. Products with different microstructural

topographies all have good qualities without visible spring-back. This suggests that, even without

a phase transformation, the residual stress in the part could be eliminated by holding and

quenching within closed cold dies.

3.5 Microstructural distribution analysis

3.5.1 Hardness testing

Hardness testing was conducted on as-formed parts, to confirm complete martensitic

transformation had been achieved through the cross-section of the prior hot zone, and to detect

the microstructural distribution along the length of parts which have been selectively heat treated.

The Vickers hardness values of the studied boron steel are ≥475 HV for martensite and 160 HV

for as-delivered initial phase [21].

Hardness values from twenty positions through the cross-section of an S-320mm formed part are

plotted in Figure 3.10. The numbering of locations for indentation on the half section (Side A) is

shown in the figure. Due to the section being symmetrical, the numbering system is mirrored on

side B. It can be seen that all hardness values are 520±20 HV, indicating a full martensite

distribution along the section. This implies good contact between the hot part and tool.

54

Figure 3.10 Hardness distribution through a cross-section of an S-320mm as-formed part

Hardness tests were undertaken along the lengths of the top surfaces of flanges, 1.5mm from the

edges, of S-60mm and S-100mm formed parts. In Figure 3.11, values of Vickers hardness are

plotted on a length scale, where the beam mid-length is taken as origin. For both the parts, full

martensite was achieved in the prior hot zones with hardness values of 520±10 HV, which

suggests full austenitization have been achieved in pre-heating. Away from hot zone at both sides,

the inter-zone regions with gradually decreasing hardness values are transition zones having

graded multiphase microstructures. The region with almost constant hardness values of 175±5HV

at left end indicates that the initial phase retained without phase transformation. Hardness values

on the right side show a little higher level for each part. This was due to a higher temperature at

the back of the heating blocks in the furnace resulting from reduced air convection.

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10

Ha

rd

ness

(H

V)

Location number

Side B

Side A

Side A Side B

1 2

3

3

7

6

5

4

8 9 10

3

55

Figure 3.11 Hardness distributions along the longitudinal direction of S-60mm and S-100mm as-

formed parts

3.5.2 Microstructural observation

In order to further confirm the tailored microstructural distribution, assumed from hardness tests,

in the selectively heat treated parts, microstructural observation were carried out on an S-100mm

as-formed part. According to the hardness distribution in Figure 3.11, the left side of the beam

can be divided into three zones having different microstructures: initial phase zone (-160mm – -

80mm), multiphase zone (-80mm – -50mm), and martensite zone (-50mm – mid-length). For

each zone, a piece of steel was cut from the flange area and sectioned through thickness for SEM

(Scanning Electron Microscope) observation. Typical micrographs for the three phase states are

presented in Figure 3.12.

0

100

200

300

400

500

600

-160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160H

ard

ness

(H

V)

Longitudinal distance to mid-length (mm)

As-delivered

Martensite

S-100mm

S-60mm

56

Figure 3.12 Typical SEM micrographs of boron steel from different microstructure zones

(sampled from flange edge) of an S-100mm as-formed part

3.5.3 Discussion

Microstructural distribution varies with many factors consisting of both material thermal

properties and thermal conditions, such as thermal conductivity of the alloy, distribution of

heating temperature, and soaking time. Besides control of the martensite and initial phase, there

is much room to grade the microstructures in transition zones. For example, in this work, the

gradient of hardness corresponding to warm zones was affected by air convection.

In this section, graded microstructural distribution in as-formed parts achieved through the

selective heating and press hardening strategy are presented qualitatively, and the feasibility of

microstructural design by tuning thermal conditions is demonstrated. This provides the basis for

57

optimising structural properties of a part. To attain the tight quantitative process control required

to optimise mechanical property distribution, the relationships between thermal conditions and

microstructure, as well as microstructure and mechanical properties, must be known. This is

achieved in the studies of fundamental mechanics of austenite formation reported in following

chapters.

3.6 Structural performance assessment

3.6.1 Three point bending tests

To assess the load bearing performance of the as-formed parts, three point bending tests were

conducted on an INSTRON (5585H) 250KN universal test machine. The flex fixture can be seen

in Figure 3.13. The beams were 320mm long, loaded in the middle by an indenter with 40mm

diameter. The indenter speed was 0.5mm/s.

3.6.2 Results and discussion

Figure 3.13 shows the failure modes of as-formed boron steel beams with different

microstructural topographies. For beams with a uniform microstructure, failure took place at the

indenter, where the bending moment was the maximum. For beams with graded microstructures,

the local instability initiated at a position away from the hard (martensite) zone, in a region

associated with mixed microstructural phases and therefore a range of mechanical properties.

This suggests that the deformation mode of a part can be adjusted through microstructural

arrangement, for specific functional requirements.

58

Figure 3.13 Failure modes under bending for boron steel parts having different microstructural

topographies

(a) (b)

Figure 3.14 Load bearing performance of boron steel parts having different microstructural

topographies: (a) Load deflection curve (b) Stroke at the onset of instability against the

proportional length of full martensite phase

0

2

4

6

8

10

12

14

16

0 4 8 12 16

Lo

ad

(K

N)

Stroke (mm)

S-320mm, Martensite

S-100mm S-60mm

S-0mm, Initial phase

0

4

8

12

16

0 0.2 0.4 0.6 0.8 1

Str

ok

e a

t p

ea

k l

oa

d (

mm

)

S/L

00.18750.31251

Initial phase

S-60mm

S-100mm

Martensite

Martensite Initial phase

S-100mm S-60mm

59

Figure 3.14 (a) shows the load deflection curves of the beams corresponding to the four

microstructural topographies. The fully hardened beam (S-320mm) sustained the highest load

which was about three times that for the beam with initial phase (S-0mm). The beam S-100mm

endured a lower load than beam S-320mm but deformed more before onset of instability. This

behaviour can be attributed to the existence of advantageous portions of strong and ductile

regions in the beam. Figure 3.14 (b) shows the relation between degree of stable deformation and

length of full martensite phase. Three data points are plotted for each condition. From the curve it

can be inferred that the greatest energy absorption (high load and large stable deformation) is

obtained for an S/L value of between 0.6 and 0.7. In addition, the performance of a beam with

tailored properties might be improved if it contained a more symmetrical microstructural

distribution and a better graded multiphase zone.

Since the functional requirements are various in a car-body, the implementation of tailored

solutions should always be adapted to a specific requirement and load situation in applications.

This will be facilitated by the accurate prediction of material behaviours through materials

modelling, which again addresses the importance of further fundamental studies.

3.7 Summary

In this chapter, selective heating and press hardening strategy has been successfully implemented

in a hot stamping operation. Demonstrator parts with either full martensite phase, full initial

phase, or differentially graded microstructures, and of apparent high quality, have been formed.

Microstructural distributions in as-formed parts have been exhibited by hardness testing and

SEM microscopy. The structural performance of as-formed parts under three point bending has

been determined.

60

CHAPTER 4 EXPERIMENTAL PROGRAMME OF

FUNDAMENTAL TESTS

4.1 Introduction

In this chapter, following the experimental studies for proving the feasibility of the selective

heating and press hardening strategy, three sets of fundamental tests are introduced. The first is

heat treatment testing to investigate the austenite formation in the boron steel during heating; the

second is hot uniaxial tensile testing to characterise the thermo-mechanical properties of the

boron steel, in the austenite phase and initial phase, corresponding to hot stamping conditions;

the last is uniaxial tensile testing at room temperature combined with hardness testing and

microstructural observation, which is to study the effects of strain rate and phase composition on

the mechanical properties of press-hardened boron steels.

All specimens used for the tests were machined from the same batch of as-delivered, 1.6mm

thick, boron steel sheet. Information on properties of the sheet is provided in Chapter 3. The

individual experimental programme and related testing facilities are introduced in the following

sections. In order to prove the repeatability, at least three tests were completed for each test

condition for all the three sets of experiments.

4.2 Austenite formation

The objective of this set of experiments is to gain a better understanding of the kinetics of the

austenite formation in the boron steel, and evaluate the effects of heating rate and soaking

temperature on the process. The formation of austenite under both continuous heating and

isothermal soaking conditions, which were designed to accord with the thermal cycle of selective

61

heating for hot stamping processes, has been investigated through heat treatment tests and

dilatometry.

4.2.1 Test equipment and specimen design

A Gleeble 3800 thermo-mechanical materials simulator was employed for the heat treatment tests.

It consists of a control console, a test chamber (shown in Figure 4.1) and a control computer.

The fully integrated digital closed loop controlled testing system ensures accurate process control,

and has the capability for phase transformation to be monitored using a dilatometer.

Figure 4.1 Gleeble 3800 thermo-mechanical materials simulator

Figure 4.2 (a) illustrates the test set-up in the chamber. For testing, the strip specimen (No.1) was

fixed between the grips (No.4), where it was resistance heated with a large alternating current at

a low voltage. Copper grips (No.4) enabled fast quenching of specimen through contact heat

transfer and ensured better stability than air/water quenching. For presentation in the figure, the

specimen (No.1) was taken out from the grips, the attachment of the dilatometer (No.2) and

thermocouples (No.3) can thus be seen. A high resolution dilatometer (No.2) was employed to

62

measure the width change of specimen during thermal cycles, from which the phase

transformation can be detected. A pair of K-type thermocouples (No.3), which enables accurate

temperature measurement up to 1573K, was used to provide signals for feedback control of

specimen temperatures.

1-Specimen; 2-Dilatometer; 3-Thermocouples; 4-Grips

(a) Test chamber and specimen with dilatometer and thermocouples attached

(b) Specimen design (dimensions are in mm, gauge length is 20mm) with schematic dilatometer

and a pair of thermocouples attached

Figure 4.2 Test set-up and specimen design

Figure 4.2 (b) schematically shows the specimen design and the location of attachments in detail:

The initial width of the specimen was 10mm; subtracting a 30mm long gripping section at each

side, the gauge length was 20mm. The reason for defining the short gauge length was to enable

63

quick heat transfer during the quenching process. The dilatometer was clamped in the middle of

the specimen so as to measure width change. The thermocouples were welded on the centre of a

specimen surface.

4.2.2 Test programme

Heat treatment conditions were designed to match the thermal cycle used in practice for hot

stamping of boron steels, which comprises continuous heating, isothermal soaking and quenching.

Figure 4.3 shows the test programme of heat treatments with different heating conditions.

Figure 4.3 Test programme of heat treatments with different heating rates and soaking

temperatures

Starting from a given initial microstructure, the heating rate and soaking temperature are the two

critical factors which affect the kinetics of austenitization. In order to study the effects of them

under both non-isothermal and isothermal conditions, two groups of test programmes were

designed. In the first group, specimens were heated to 1173K at different heating rates from

673K (the heating rate has no influence at lower temperature). Long soaking periods were given

64

to enable thermodynamic equilibrium to be achieved. These were 10min for 1K/s and 15min for

5K/s and 25K/s. In the second group, specimens were heated at the heating rate of 5K/s to

different soaking temperatures of 1023K, 1073K, 1123K, and 1173K, and soaked for 15mins to

enable the austenite formation taking place.

In addition, a separate test programme was designed for the third group: a specimen is heated up

to 1273K at a heating rate of 2K/s and soaked for 2 minutes without reaching saturation of

austenite. This test was used for the validation of austenite formation model which is presented in

Chapter 6.

After specimens were subjected to the designed heating and soaking periods, all of them were

quenched at a cooling rate of 50K/s, which ensured complete transformation from austenite phase

to martensite phase. The critical cooling rate for martensitic transformation from austenite is

27K/s, according to the material supplier.

4.3 Thermo-mechanical properties at elevated temperatures

The objective of performing this set of experiments was to simulate the deformation of the boron

steel in a state corresponding to hot stamping after selective heating, so as to characterise the

effects of temperature and strain rate on its viscoplastic behaviour. The thermo-mechanical

properties of the boron steel in two representative microstructural states, austenite and the initial

phase (ferrite and pearlite), have been studied through hot tensile tests.

4.3.1 Test equipment and programme

The Gleeble 3800 materials simulator was employed for the hot tensile tests. It has a load

capacity of 100kN and a maximum stroke rate of 2m/s in tension. As for the set-up for heat

treatment tests, specimens were mounted between grips in the chamber, heated and stretched.

65

The dilatometer and thermocouples were used to measure width changes and temperatures of

specimens, respectively.

Figure 4.4 Temperature-time profiles for isothermal tensile testing of boron steels in both

austenite (soaked at 1173K) and the initial phase (soaked at 923K)

Figure 4.4 presents two groups of temperature-time profiles designed for isothermal tensile

testing of the boron steel in the austenite and initial phase at elevated temperatures. In the first

group, the heating route was suggested by the steel supplier for full austenite formation: 15K/s

heating rate, 1173K soaking temperature and 5 minutes soaking time. In the second group, the

soaking temperature was defined as 923K, which ensured no phase transformation taking place

during the heating process. According to the real condition of selective heating, a lower heating

rate of 8K/s was defined. In order to make sure the heating periods of the two groups were of

same length (6 minutes), soaking time was determined as 4 minutes and 38.75 seconds. After the

heating step, specimens were quenched to a certain temperature for isothermal deformation.

Cooling rates of 40K/s and 32K/s were defined for the austenite and the initial phase respectively,

66

which are similar to the real corresponding cooling rates during transfer of work-pieces to dies in

practice.

The isothermal uniaxial tensile tests were conducted at various temperatures and strain rates,

within a temperature range of 873K to 1073K for austenite and 723K to 923K for the initial

phase, and a strain rate range of 0.005/s to 5/s for both, to cover the typical conditions for hot

stamping of boron steels. Matrices of test programme for the two phase states are listed in Table

4.1.

Table 4.1 Test programme (‘√’ represents the selected test conditions)

Temperature

(K)

Strain rate (/s)

0.005 0.05 0.5 5

Austenite

1073 √

973 √ √ √ √

873 √

The initial phase

923 √ √ √ √

823 √

723 √

67

4.3.2 Specimen design and test procedure

4.3.2.1 Specimen design

The design of the dog-bone type specimen is shown in Figure 4.5. The width and parallel length

of the gauge section were 6mm and 30mm, respectively. Specimens were machined from the

same piece of as-delivered sheet in the rolling direction.

A dilatometer was clamped in the middle of the specimen to measure the width strain associated

with deformation. Three pairs of thermocouples were welded on the mid-width line of the

specimen along the gauge section: T1-mid-length, T2-5.5mm from mid-length, and T3-11mm

from mid-length. T1 was used to control specimen heating, T2 and T3 were used to monitor the

temperature distribution along the specimen in the longitudinal direction.

Figure 4.5 Specimen design (dimensions are in mm) with schematic dilatometer and three pairs

of thermocouples attached

4.3.2.2 Temperature gradients in the longitudinal direction

Due to the resistance heating conditions on Gleeble, the temperature is not uniformly distributed

along the gauge length. It reached the highest value, equal to the programme controlled

temperature, at the midway and dropped gradually to both sides. Since the failure position for

68

many tests did not precisely lie on the middle of specimen, it was important to evaluate the error

by detecting the temperature gradient.

Figure 4.6 (a) and (b) respectively present the temperature distributions measured using

thermocouples T1, T2 and T3 for the deformation of austenite and the initial phase at different

testing temperatures. For the testing on austenite in Figure 4.6 (a), assuming temperature

distributions were symmetric with respect to the mid-length of a specimen for any testing

temperature, the temperature drop of less than 10K could be achieved within ±1mm offset from

mid-length. Thus, to ensure the accuracy of testing results, only tests with failure taking place

within this offset were taken as valid. Similarly, the threshold for the testing on initial phase, in

Figure 4.6 (b), was within ±1.5mm.

(a) Testing on austenite (b) Testing on the initial phase

Figure 4.6 Temperature distributions along the specimen in the longitudinal direction at different

testing temperatures

4.3.2.3 Control of strain rate

True (also called natural or logarithmic) strain is adopted for the analysis of large deformation at

elevated temperatures in this study. Accurate control of true strain rate is vital for the

573

673

773

873

973

1073

1173

1273

0 5.5 11

Tem

pera

ture (

K)

Distance to mid-length (mm)

T1 T2

T3

523

623

723

823

923

1023

0 5.5 11

Tem

pera

ture (

K)

Distance to mid-length (mm)

T2 T1

T3

69

characterisation of strain rate effects on the viscoplastic behaviour of the boron steel. Efforts have

been made to achieve high accuracy in two aspects:

Ensure constant true strain rates

Constant testing speed cannot achieve constant true strain rate during deformation. The true

strain in the longitudinal direction (effective true strain) can be determined from the dilatometric

measurement by:

0 0

2ln( ) 2ln(1 )

T

W W

W W (4.1)

where W0 is the initial specimen width, W is the instantaneous width, and ΔW is the dilatometric

measurement (the width change). However, real-time strain rate control based on the dilatometric

measurement was not practical on the testing machine. Therefore, length control was made by

defining a stroke-time curve in the test programme based on true strain definition. It was given as:

0 exp( ) 1 Tl l t

(4.2)

where l0 is the initial specimen gauge length, Δl is the stroke (the length change), t is time, and

𝜀�� is the defined true strain rate. Thus the specimen could be tensioned at a constant true strain

rate before necking took place.

Determine effective gauge length for proper input

Due to temperature gradients, the steel experienced different extents of deformation at different

sections. Figure 4.7 presents a fractured specimen. The locations of T1, T2, T3 and end of

parallel length, which were initially 0, 5.5mm, 11mm, and 15mm from mid-length, reveal that

larger deformation occurred closer to the mid-length. Therefore, if the stroke-time curve is given

by taking the parallel length 30mm as l0 in formula (4.2), the real strain rate measured in the mid-

70

length will be much larger than the defined 𝜀��. To realize the defined value of strain rate in the

middle of specimen, a smaller l0 should be defined, as the effective gauge length, to determine

the input stroke-time curve.

Figure 4.7 Deformation on a fractured specimen

A method to determine the effective gauge length by trial and error was proposed: for a test

condition of defined true strain rate 𝜀��, firstly, the input stroke-time curve was determined by

giving an initial value of effective gauge length 𝑙0 (can be 30mm). Then, the real value of true

strain rate 𝜀��′ was determined by linear regression of true strain and time (the section before

necking), where the data of true strain with time was obtained from dilatometric measurement

(equation (4.1)). Last, a corrected value of effective gauge length (𝑙0′) was updated by: 𝑙0

′ =

𝑙0𝜀��/𝜀��′. Higher accuracy can be achieved through more iteration. It is noted that a fixed value of

effective gauge length could not meet all the test conditions. This was because the temperature

gradient varied with the value of control temperature (see Figure 4.6); in addition, even for a

same temperature gradient, the strain distribution varied with the deformation rate due to

viscoplastic properties. With consideration of the efficiency, determination of l0 for each test

condition is not necessary. In this work, a value of 20mm was defined, whereby variations of

strain rates from designed values were small for all tests. To enhance the accuracy of result

analysis and materials modelling, the real value of strain rate that each specimen experienced

could be calculated individually according to test measurements.

71

4.4 Mechanical properties at room temperature

This set of experiments was designed to investigate the mechanical properties of the boron steel

consisting of different microstructural phases, for a large range of deformation speeds at room

temperature. This was in order to evaluate the crashworthiness of press-hardened boron steel

parts having graded microstructural distributions. The experimental work can be divided into two

groups: the first group is to characterise the effect of strain rate on the tensile properties of the

martensite phase and also the initial phase (ferrite and pearlite), of the boron steel via both quasi-

static and dynamic tensile testing; the second group was to study the effect of phase composition

(volume fraction of martensite) on the mechanical properties via quasi-static tensile testing,

hardness testing and microstructural observation.

4.4.1 The first group: tensile testing over a range of strain rates

Boron steel in both martensite and the initial phase were tested over a wide range of strain rates

from 0.001/s to 500/s which is relevant to a typical vehicle crash [125-127]. Common quasi-static

material testing is in the range of strain rates 10-4–10-1/s; dynamic testing starts at strain rates

above 10-1/s when inertia effects become important [126]. When strain rate is above 102/s, which

is normally classified as high rate testing, the effect of stress wave propagation should be

considered [126, 128]. The stress oscillation caused by the impact of loading system increases

with increasing strain rate [128, 129]. In order to obtain valid stress-strain data over the whole

testing range, a careful selection or design of the testing machine, clamping system, specimen,

and measurement method is critical.

72

4.4.1.1 Design of experiment and specimen

Testing machines

For testing at quasi-static conditions, a screw-driven INSTRON testing machine was used. It had

250kN load capacity and 0.001–500mm/min speed range.

For dynamic testing, a servo-hydraulic high rate INSTRON testing machine was employed. It

was capable of loads up to 20kN and velocities up to 25m/s.

Stress measurement

Stress during tension was obtained by measuring load by different means. For quasi-static testing,

the load was simply measured through the machine-inbuilt strain gauge load cell. For dynamic

testing, a commercial piezoelectric load washer with higher response frequency was adopted. It

was able to provide accurate measurement when the testing rate was relatively low. With

increasing testing speed, in order to reduce the stress wave propagation effect, the load cell

should be placed as close as possible to the specimen [126]. Thus, for the strain rate of 50/s and

more, a strain gauge was attached to a gripping section of a specimen to create a transducer and

directly measure the load. This measurement method resulted in reduced load oscillations and

provided increased frequency response.

Strain measurement

Conventional contact strain measurement (e.g. extensometer) is not applicable for high rate

tensile testing due to inertia effects and low response characteristics [130]. Therefore, an optical

technique of DIC (digital image correlation), in which the movement of coloured spatters sprayed

on a specimen are recorded with a camera, was adopted in this work. For dynamic tensile testing,

a PHOTRON SA-1 digital high speed camera was employed. It was capable of 5,400 fps (frames

73

per second) for full resolution of 1024×1024 pixels, and up to 675,000 fps maximum by reducing

resolution to 64×16 pixels [131].

Specimen design

Figure 4.8 shows the geometry of the dog-bone type specimen for the tests: the gauge width was

3mm and the parallel length was 18mm. The reasons for designing a small specimen were: for a

certain testing speed, a smaller parallel length enables a higher strain rate; since the martensitic

boron steel is of ultra-high strength, the gauge width should be small enough to ensure the

specimen fractured within the 20kN load capacity; with consideration of the second group of

tests, a small gauge section was required to ensure uniform microstructural distribution (detailed

explanation of this is given in section 4.4.2.1). For strain gauge attachment, the tensile specimen

was designed with a longer grip section at one end. The position of the strain gauge on a

specimen can be seen in the figure.

Figure 4.8 Specimen design (dimensions are in mm) with a schematic strain gauge attached

Test programme

Boron steels in each of the two phase states were tested under the same conditions. For each one,

the designed strain rates, as well as the corresponding testing machine and stress/strain

measurement devices, are listed in Table 4.2. It is to be noted that all the defined strain rate

values refer to initial strain rates under the constant speed control used in this set of tests.

74

Table 4.2 Matrix of test programme and facilities

Strain

rate(/s)

Tensile Speed

(mm/s)

Testing

Machine Stress measurement

Strain

measurement

0.001 0.018 Screw-driven

INSTRON

Conventional strain gauge

load cell

Digital Image

Correlation

(DIC) 0.05 0.9

5 90

Servo-hydraulic

INSTRON

Piezoelectric load washer

DIC with high

speed camera

50 900

Strain gauge attached on

specimen 200 3600

500 9000

4.4.1.2 Specimen preparation

The preparation of specimens was complicated and of great importance in this work. The

procedure was divided into four steps as follows (step 3 was needed only for strain rates 50-

500/s):

Step 1 - Heat treatment

To obtain full martensite phase and the initial phase (ferrite and pearlite) equivalent to the press

hardened state, as-delivered boron steel sheets were respectively heated in a furnace to 1173K

and 993K for 5-minute soaking, and then quenched using cold steel blocks.

Step 2 - Machining

The heat treated sheets were machined into tensile specimens using Wire EDM (Electrical

Discharge Machining). The edges of gauge sections were polished to remove machining affected

material or geometric defects.

75

The manufacturer applied coating on one surface of the specimen gauge section was removed

using a sandblaster (the reason is explained in step 4). The influence on material strength was

negligible.

Step 3 - Strain gauge attachment

To measure the load during tensile testing at high rates, a strain gauge was mounted on the

specimen. The procedure is outlined: First, strain gauge was positioned in the gauging area of

specimen (shown in Figure 4.8), which had been carefully cleaned, and adhesive was applied.

Perfect alignment along the midline was required for data accuracy. Second, the specimen, with

pressure applied on the gauging area using a spring clamp, was cured in a furnace at 383K for 4

hours for thorough bonding of the strain gauge. Last, lead-wires were soldered to the strain gauge

tabs in order to make electrical connections to strain gage circuits for testing.

Step 4 - Painting

To measure the strain during testing, the specimen surface was stochastically marked by a white

spray against a black painted background. The speckle patterns provided grey scale contrast for

the image correlation method [132]. The paint was applied to the steel surface with the

manufacturer’s coating removed, because the coating tended to become detached under large

deformations, due to its low ductility at room temperature.

4.4.1.3 Set-up and procedure for quasi-static tensile testing

Figure 4.9 shows the set-up for quasi-static tensile testing. Tests were performed on the screw-

driven INSTRON testing machine. The INSTRON control system was used to determine the

strain rate by controlling the crosshead speed, and record the load data measured by the strain

gauge load cell equipped in the machine. A DIC (Digital Image Correlation) integrated system

was set up to measure the strain field during the testing. For the flat specimen, just one camera

76

was needed for two-dimensional DIC. The frame rate of camera was set as 1 fps and 25 fps for

the strain rate of 0.001/s and 0.05/s, respectively. Two LED lights were employed for

illumination. In the DIC control system, the analytical tool ARAMIS was used to run the sensor

and controller, and process strain measurements.

1-Screw driven INSTRON machine; 2-INSTRON control system; 3-Cameras and LED lights;

4-DIC control system; 5-Specimen and the DIC focused gauge section

Figure 4.9 Set-up of facilities and specimen for low rate tensile testing

The enlarged view of No.5 in Figure 4.9 shows the initial state of a specimen with stochastic

speckles and the DIC processed strain field on the gauge section. To avoid the geometry effect of

the shoulders and ensure uniform deformation distribution before necking, the gauge length was

defined as 15mm, which was less than the parallel length of 18mm. Engineering strain in tensile

tests is given by:

0

1 E

L

L

(4.3)

where L0 is initial gauge length and L is the instantaneous gauge length. Values of L could be

obtained through DIC post-processing, thus the evolution of engineering strain with time was

obtained.

77

1-Control system of the Servo-hydraulic INSTRON; 2-Actuator; 3-Slack adaptor; 4-Grips;

5-Strain gauge; 6-Piezoelectric load washer; 7-Strain gauge load cell;

8-Strain gauge transducer amplifier; 9-Amplifier; 10-Multimeter; 11-Digital work station;

12-High speed camera; 13-Lighting system; 14-DIC control system; 15-Specimen

Figure 4.10 Set-up of facilities and specimen for dynamic tensile testing

78

4.4.1.4 Set-up and procedure for dynamic tensile testing

Figure 4.10 shows the experimental set-up for dynamic tensile testing carried out on the servo-

hydraulic INSTRON machine. The elements in the figure can be classified into three systems

according to their functions: the dynamic system, marked in red, is for the loading of specimens;

the data acquisition system, marked in blue, is for recording signals of load and actuator

displacement; the DIC (Digital Image Correlation) system, marked in green, is for strain

measurement. Arrows indicate the direction of control commands or data flow. Sub-figure (b) is

the partially enlarged view of (a), and (c) is the partially enlarged view of (b). Details about each

system are explained as follows:

Dynamic system

For the dynamic loading process, proper input speed and clamping mechanism are critical to

ensure the accuracy of data [130]. Figure 4.10 shows the load train which consists of an actuator

(No.2, see sub-figure (a)), a slack adaptor (No.3, see sub-figure (a)), a pair of grips (No.4, see sub-

figure (c)) and a specimen (No.15, see sub-figure (c)). They were carefully clamped in good

alignment to avoid bending moments on the specimen.

In the dynamic system, the input testing speed was defined in the control system (No.1), and the

load was applied through the actuator (No.2) driven by hydraulic pressure. To achieve high range

of strain rates, the servo-hydraulic machine was in open loop mode which did not have instant

feedback for accurate speed control. Nevertheless, the machine could maintain nearly constant

speed over a certain distance in open loop. Therefore, the initial position of the actuator was

adjusted, such that the dynamic testing was performed within the constant speed window. In

addition, because that constant speed wasn’t exactly equal to the input speed, the input speed was

calibrated through trial and error for each testing condition. The deviation in the real testing

speed and the required speed has been controlled within ±5% error.

79

The slack adaptor (No.3) is normally a critical device for high rate testing in open loop system

[130]. It consists of a hollow tube connected to the actuator (No.2) and a sliding bar connected to

the top grip (No.4). In the testing, the hollow tube travels freely to accelerate before its end

contracts the top of the sliding bar, thus a specific testing speed could be reached before loading

the sample. A rubber washer, placed at the end of the hollow tube, was used to dampen

oscillations from the impact [133].

The specimen (No.15) was mounted by a pair of lightweight grips (No.4) which was specially

designed in order to reduce the inertia effects.

Data acquisition

All signals of load and actuator displacement were fully integrated within the data acquisition

system. Shown in Figure 4.10, three items for stress measurement were aligned in the load train:

a strain gauge transducer (No.5, see sub-figure (c)), a piezoelectric load washer (No.6, see sub-

figure (b)), and a machine-equipped strain gauge load cell (No.7, see sub-figure (b)). The signal

from the strain gauge (No.5) was converted and amplified through a strain gauge transducer

amplifier (No.8); the signal from the piezoelectric load washer (No.6) was amplified by another

amplifier (No.9). See Figure 4.10 (a), both the signals from No.5&8 (Channel I) and No.6&9

(Channel II) were monitored by a digital work station (No.11); the signal from No.7 was

monitored by the INSTRON control system (No.1). The position of the actuator (No.2) was

tracked internally through a linear variable differential transformer (LVDT) in the INSTRON.

This signal was also imported into the digital work station as Channel III and set up for trigger

control. During testing, the digital work station was triggered by the actuator displacement, just

prior to the contact of the hollow tube and the sliding bar, to realize synchronous recording of the

three signal-channels.

80

To determine the load, conversion from the signals of voltage recorded by the digital work

station to forces was required. Regarding Channel I, calibration was made for each specimen

right before each testing. The procedure was: first, the strain gauge transducer amplifier (No.8)

was connected to a multimeter (No.10). Second, the specimen was gently stretched within the

elastic deformation range by controlling the actuator manually, while a range of force and voltage

values were recorded. The value of force was read from INSTRON control system (No.1)

measured by the strain gauge load cell (No.7), and the corresponding value of voltage was read

from the multimeter. Last, the ratio between loading force and the output of strain gauge

transduce amplifier was determined through linear regression of the recorded numbers.

Regarding Channel II, the ratio between force and voltage was available from calibration results

given by the device manufacturer. For tensile testing at strain rate 5/s, the stress was calculated

from the measurement of piezoelectric load washer (Channel II). In this case, the strain gauge as

well as relevant devices and procedure were not needed. For tensile testing at strain rates 50-

500/s, stress was calculated from the measurement of the strain gauge transducer (Channel I).

Nevertheless, the piezoelectric load washer was retained for the consistency of set-up.

The signal of actuator displacement in the digital work station (Channel III) was also calibrated.

For a certain position of the actuator, the corresponding values of displacement and voltage were

read from the INSTRON control system and the digital work station, respectively. Based on a

range of reading numbers, the ratio was determined through linear regression. The converted data

of actuator displacement was used to check real testing speeds.

DIC system

DIC system was employed for strain measurement. Shown in Figures 4.10, it consisted of a high

speed camera (No.12), a lighting system (No.13) and a control system (No.14). The high speed

camera was used to track specimen deformation. The frame rate and resolution of the camera

81

were adjusted according to test conditions. Limited by the device capacity, for high rate testing,

the frame rate could be increased only by reducing resolution. For example, testing on martensite

specimen at 500/s strain rate lasted less than 0.3ms, so the frame rate was set as 108,000 fps to

obtain about 30 frames of images during specimen deformation, while the corresponding

resolution was just 768×64 pixels. The trade-off between sampling rate and image accuracy had

to be carefully weighed. To minimise heating of the sample, the lighting system was switched on

just prior to testing. The control system was used to run the camera and record images. Images

were imported into ARAMIS for DIC post-processing. The way to calculate the strain was same

as that for quasi-static testing described in sub-section 4.4.1.3.

4.4.2 The second group: tensile testing over a series of phase compositions

Boron steels with a series of phase compositions (martensite volume fraction from 0 to 100%)

were tested under a quasi-static condition (strain rate 0.001/s). Heat treatments were performed to

produce specimens having various microstructures; microstructure analysis was conducted to

quantify the phase composition of specimens.

4.4.2.1 Specimen design and preparation

Figure 4.11 shows the geometry of the dog-bone type tensile specimen in solid line. It was

designed to be consistent with the specimens in the previous group: 3mm gauge width and 18mm

parallel length (15mm gauge length). Since no strain gauge was required, the two gripping

sections were of the same length.

82

Figure 4.11 Design of specimens (dimensions are in mm) for quasi-static tensile testing (solid

line) and Gleeble heat treatments (dash line)

A Gleeble 3800 material simulator was employed for steel heat treatment due to its accurate

process control. However, the temperature gradient due to resistance heating was not desirable

because the microstructure distribution in the gauge section of tensile specimens had to be

uniform. When a dog-bone type specimen was heated in the Gleeble, there were large

temperature gradients along the gauge length, especially at the locations close to shoulders.

Therefore, a design of rectangular specimen with large length (dashed line in Figure 4.11) was

adopted. In addition, stainless steel (instead of copper) grips with smaller thermal conductivity

were employed. In this case, the temperature variations in the region 9mm from mid-length,

which corresponded to the parallel length of the tensile specimen, were controlled within 5K.

The as-delivered boron steel specimens were heated to different temperatures (993K–1173K) at

the heating rate of 15K/s and soaked for 5 minutes, in order to achieve different extents of

austenitization. The cooling rate of 50K/s was defined to enable complete transformation from

austenite to martensite. Thus, quenched boron steel specimens having different fractions of

martensite were obtained.

A series of soaking temperatures (993K, 1023K, 1053K, 1083K, 1113K, 1143K, and 1173K)

with the even increment were firstly selected for heat treatments. Based on the preliminary results

83

of tensile testing, a critical temperature range was identified. Then, more soaking temperatures

(1063K, 1068K, 1073K, 1078K, 1093K, and 1103K) were sampled for further investigation.

Heat treated specimens were machined to obtain tensile specimens. Two small pieces cut from

the middle section of each specimen were kept. Figure 4.12 shows the test-pieces of different

parts used for different testing. The specimen preparations for tensile testing were conducted

according to the step 2 and step 4 introduced in subsection 4.4.1.2.

Figure 4.12 Test-pieces for different testing

4.4.2.2 Test procedure

Quasi-static tensile testing of specimens having different phase compositions (corresponding to

the 13 soaking temperatures) was conducted at a strain rate of 0.001/s. The test equipment and

procedure was same as that described in sub-section 4.4.1.3.

According to tensile results, representative specimens corresponding to soaking temperatures of

993K, 1023K, 1063K, 1068K, 1073K, 1083K, 1113K, 1143K, and 1173K were selected to

measure hardness and phase composition. At least five indents were made on each specimen for

measuring the hardness. Microscopic images, obtained from SEM observation, were processed

using a commercial software Image-J for measuring the volume fraction of martensite.

84

CHAPTER 5 EXPERIMENTAL RESULTS AND

DISCUSSION

5.1 Introduction

This chapter contains detailed results obtained from the three sets of experiments described in the

previous chapter. Moreover, discussion and analysis are conducted to characterise the material

behaviour under hot stamping conditions and in automotive crash scenarios. First, based on the

results of heat treatment tests, the effects of heating rate and temperature on the austenite

formation are rationalised. Second, based on the results of hot tensile tests, the viscoplastic

deformation behaviour of boron steels (austenite and initial phase) is discussed in terms of strain

rate and temperature dependence. Last, based on the results of tensile tests at room temperature,

the strain rate sensitivity of as-formed boron steels (martensite and initial phase) is analysed;

combined with the hardness and microstructure measurements, the influence of phase

composition on tensile properties is characterised.

5.2 Austenite formation

The mechanism of austenite formation in hypoeutectoid steels is introduced first for better

interpretation of the experimental characterisation. The evolution curves of austenite volume

fraction with temperature and time are obtained from dilatometric curves. By analysing the

evolution curves, the effects of heating rate and temperature on the progress of austenite

formation under both non-isothermal and isothermal conditions are investigated.

85

5.2.1 Mechanisms of austenite formation in hypoeutectoid steels

(a) Fe-C equilibrium phase diagram

(b) The phase transformation process

Figure 5.1 The formation of austenite in a hypoeutectoid steel (containing less than 0.76 wt% C)

(a) Fe-C equilibrium phase diagram (b) Phase diagram of hypoeutectoid steel and the schematic

representations of the microstructure evolution

86

A study of the constitution and structure of steels normally starts with the Fe–C equilibrium

diagram [134]. Figure 5.1 (a) shows the equilibrium condition for thermodynamically distinct

phases. According to the carbon content of the studied steel, only the hypoeutectoid part of the

equilibrium diagram, where 0.02 < wt% C < 0.76, is studied in this paper. Regarding this part,

there are two features which are critical: first, the temperature Ae1 at which the eutectoid reaction

occurs; second, the temperature Ae3 at which the ferrite (α) can fully transform to austenite (γ).

The Ae1 is normally a single temperature above 973K and does not change with carbon content,

whereas the Ae3 is about 1183K for pure iron and progressively decreases with increase in carbon.

This is because the solubility of carbon in ferrite (α) is low and ferrite alone can begin to

transform to austenite (γ) only at high temperature, but if cementite decomposes and yields its

carbon to the transformation front, the reaction from ferrite to austenite can proceed at lower

temperatures [106, 134].

However, preheating steel is a continuous operation for most practical hot forming applications

[107]. The formation of austenite in a hypoeutectoid steel generally involves heating an

aggregate of ferrite and cementite (α + θ) through two phase (α + γ) region into a single austenite

(γ) phase. In this condition, the equilibrium diagram is not valid and beginning and end of the

transformation are shifted to higher temperatures Ac1 and Ac3 which are sensitive to the heating

rate [106, 134]. Therefore, as shown in Figure 5.1(b), the phase diagram is modified for

transformations that occur in continuously increasing temperature conditions [135]. The

formation of austenite in a hypoeutectoid steel during continuous heating is schematically

illustrated. In Figure 5.1 (b-1), the initial microstructure of the steel is composed of pro-eutectoid

ferrite (α) and pearlite, the latter being a composite of eutectoid ferrite (α) and cementite (θ). The

phase composition of the mixture is determined by the amount of carbon in the steel. With an

increase in atom mobility and driving force during heating, the pearlite regions firstly become

unstable above temperature Ac1. In a real microstructure, a pearlite region contains numbers of

87

colonies in which lamellas of ferrite and cementite, variously spaced and oriented, are located.

Austenite nucleation primarily takes place at intersections or interfaces of pearlite colonies, and

also at interfaces of ferrite-cementite lamellae within a colony [105]. The new grains of austenite

grow into pearlite colonies to replace the eutectoid ferrite; at the same time, cementite dissolves

in the austenite. Once the pearlite is consumed (Figure 5.1 (b-2)), the reaction proceeds into the

remaining pro-eutectoid ferrite. Below temperature Ac3, the ferrite can transform to austenite only

with additional carbon provided. Carbon atoms diffuse from inside the enriched austenite grains

to γ/α interfaces and cross them, which enables the transformation from pro-eutectoid ferrite to

austenite. The γ/α interfaces gradually move towards α phase regions (Figure 5.1 (b-3)). This

process continues until temperature Ac3 is reached, when the average carbon content in austenite

becomes equal to the carbon content of the steel. The steel is then fully austenitic (Figure 5.1 (b-

4)).

5.2.2 Experimental results

When a metal undergoes a phase transformation, the lattice structure changes, which is in

principle accompanied by a change in specific volume. The formation of austenite involves the

lattice change of iron from a body-centred cubic (BCC) form to a face-centred cubic (FCC) form,

which results in a change in density and hence in volume. The evolution of austenitization can

thus be deduced from experimental results of dilatometry [97, 134, 136].

Figure 5.2 (a) and (b) show the experimentally measured width change (ΔW) versus temperature

and time, respectively. The test was carried out at a heating rate of 5K/s with soaking temperature

of 1173K for 15 minutes. The experimental curve can be divided into four stages. As can be seen

in Figure 5.2 (a), in the first stage, the dilatometric curve exhibits a linear expansion as the

temperature changes. This is a pure thermal expansion of the boron steel with the initial phase

mixture. In the second stage, the dilatometric curve deviates from linearity from 1007K (Ac1).

88

This is because the formation of austenite takes place, which contributes to the change of

specimen width. For the continuous heating stage, the curve is a result of the competition

between the volumetric change induced by phase transformation and thermal expansion. For the

isothermal soaking stage, the curve shows only contraction caused by the phase transformation

(the vertical part in Stage 2 shown in Figure 5.2 (a)). As shown more clearly in Figure 5.2 (b), the

austenite formation rate in the isothermal soaking period decreases with the soaking time. At 15

minutes of the soaking time (Figure 5.2 (b)), the width change rate tends to zero, i.e. d(∆W)/dt ≈ 0.

It can be concluded that thermodynamic equilibrium has been achieved. The microstructure ends

up as full austenite γ for this case, since the soaking temperature is above Ae3. It could be a

mixture of austenite and ferrite (γ + α) if the soaking temperature is between Ae1 and Ae3 [99, 102].

In the third stage, the curve is linear again, which reflects the pure thermal contraction of the steel

during quenching or rapid cooling. In the fourth stage, volume expansion is shown on the curve,

which corresponds to the phase transformation from austenite γ to martensite α'. Since this study

is mainly concentrated on the formation of austenite, the analysis is focused on the experimental

data in Stage 2 of Figure 5.2. The experimental results, corresponding to the section from 873K

to the end of soaking, under different testing conditions are summarised in Figure 5.3.

89

(a) Change of width against temperature (b) Change of width against time

Figure 5.2 Experimental curves showing the width change of specimen against (a) temperature

and (b) time during the heat treatment process (heating rate: 5K/s, soaking temperature: 1173K)

Figure 5.3 (a) shows the width changes of specimens (ΔW) with temperature and time,

respectively, for different heating rates and constant soaking temperature of 1173K. During the

continuous heating period (the left figure) a lower starting temperature (Ac1) and more contraction

of width due to austenitization are observed for the lower heating rate. During the isothermal

soaking period (the right figure) the width change (ΔW) for all heating rates reduces gradually

and becomes constant at a common value. This indicates that, given sufficient soaking time, the

austenite formation could be completed at a temperature of 1173K. Note, this is higher than Ae3.

Thus, the austenite formation has been completed for all the three tests. Figure 5.3 (b) again

shows ΔW of specimens with temperature and time. However these tests were carried out at a

heating rate of 5K/s and held at four different soaking temperatures of 1023K, 1073K, 1123K and

1173K for 15 minutes. During the continuous heating period (the left figure) ΔW for all tests lies

almost on the same curve, as the heating rate was common. During the isothermal soaking period

(the right figure) all the curves tend to become horizontal eventually, which shows

thermodynamic equilibrium has been virtually reached for every isothermal soaking condition. A

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

273 473 673 873 1073 1273Ch

an

ge o

f w

idth

, Δ

W (

mm

)

Temperature (K)

Stage 2

Stage 4

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 400 800 1200Ch

an

ge o

f w

idth

, Δ

W (

mm

)

Time (s)

Stage 2

90

different reduction of ΔW can be seen for each of the soaking temperatures; however, the value

of the width change (ΔW), is a function not only phase composition but also instantaneous

temperature and therefore is not an indicator of the degree of phase transformation alone.

(a) Soaking temperature: 1173K

(b) Heating rate: 5K/s

Figure 5.3 Width changes of specimens tested at different (a) heating rates (soaking temperature:

1173K), and (b) soaking temperatures (heating rate: 5K/s)

91

A transformation method has been developed to calculate austenite volume fraction based on the

experimentally measured ΔW in this study. Details are provided in Appendix 1. By using the

method, the dilatometric curves shown in Figure 5.3 can be presented in terms of austenite

volume fraction, as shown in Figure 5.4, which permits a more rational insight into the progress

of austenite formation.

Figure 5.4 (a) shows the first group of test results. The austenite formation firstly progresses

differently during continuous heating for different heating rates. When the continuous heating

ends at 1173 K, the amount of transformed austenite depends on heating rate: for 1K/s, fA = 77%;

for 5K/s, fA = 61%; and for 25K/s, fA = 54%. Subsequently, the volume fractions of austenite (fA)

keep increasing until about 100% at different rates under isothermal conditions, despite soaking

temperature being the same. Figure 5.4 (b) shows results of the second group of tests. With

increasing soaking time, the volume fraction of austenite (fA) increases and then becomes almost

constant at a value less than 100%, which depends on soaking temperature. The maximum value

of volume fraction obtained for each soaking temperature is: for 1023K, fA = 32%; for 1073K, fA

= 63%; for 1123K, fA = 92%; and for 1173K, fA = 99%.

92

(a) Soaking temperature: 1173K

(b) Heating rate: 5K/s

Figure 5.4 Variations of volume fraction of austenite with temperature and time for different (a)

heating rates (soaking temperature: 1173K) and (b) soaking temperatures (heating rate: 5K/s)

5.2.3 Analysis of full austenite formation

Phase transformation in general is controlled by two types of factors: 1) Initial microstructure,

including phase composition, chemical composition, grain size and the presence of non-metallic

inclusions; that is, the intrinsic properties of an alloy. 2) External conditions, including heating

93

rate and temperature. Assuming that the intrinsic properties of the tested boron steel were to the

supplier’s specification and the same for all specimens, this study is focused on the effects of

process conditions: heating rate and soaking temperature on the progress of austenite formation.

5.2.3.1 Effects of heating rate on non-isothermal austenite formation

It is stated in Section 2 that certain amounts of superheat above equilibrium temperatures Ae1 and

Ae3 are required to start and complete the phase transformation under non-isothermal conditions

[42, 94]. The temperature and time to start austenite formation and to attain certain volume

fraction of austenite (fA = 10% to 50%) in the heating-up stage, as measured for different heating

rates, are summarised in Figure 5.5, which is normally called a continuous heating transformation

(CHT) diagram. It is apparent that less time is required at a higher heating rate, to achieve the

same volume fraction of austenite. Figure 5.5 also shows that the starting temperature Ac1

increases with increasing heating rate. For example, at the heating rate of 1K/s, the temperature

for Ac1 is 996K, but for the heating rate of 25K/s it is 1010K. The same phenomenon can be

observed for the other volume fractions (fA = 10% to 50%), shown in Figure 5.5. This is mainly

due to the fact that a higher heating rate results in less soaking time being required for incubation

of austenite formation.

94

Figure 5.5 Continuous heating transformation (CHT) diagram

Figure 5.6 (a) shows that the relationship of heating rate and temperature for a certain volume

fraction of austenite formation (fA = 0% to 50%) is linear when plotted on log-log axes. In the

equations given for the trend lines, T is heating rate in K/s, and T is the absolute temperature in K.

For example, for 50% austenite formation, the 3 data points of temperature and heating rate can

be approximated by T50%=1084 T0.018

(the top line in Figure 5.6 (a)). The slope of the trend lines

for different volume fractions are positive and increase with increment of austenite volume

fraction. For example, for fA = 10%, the slope is 0.006, and for fA = 50%, the slope is 0.018.

These features reveal that the temperature required to attain a certain amount of austenite

increases with increasing heating rate. In addition, the effect is greater for greater amounts of

transformation.

973

1023

1073

1123

1173

0 50 100 150 200 250

Tem

pera

ture (

K)

Time (s)

25K/s

5K/s

1K/s

Ac1

10%

20%

30% 40%

50%

996K 1003K

1010K

95

(a) Effects of heating rate on the transformation temperature to attain certain volume fractions of

austenite

(b) Effects of heating rate on the transformation time to attain certain volume fractions of

austenite

Figure 5.6 Effects of heating rate on austenite formation under continuous heating conditions

Figure 5.6 (b) shows the relationship between heating rate and required time for various volume

fractions of austenite formation are again linear when plotted on log-log scales. On the vertical

axis and in the trend line equations, ∆t' is heating time increment and represents the time

973

1 10 100

Tem

pera

ture (

K)

Heating rate, (K/s)

1173

1

10

100

1 10 100

Hea

tin

g t

ime i

ncrem

en

t, Δ

t' (

s)

Heating rate, (K/s)

96

difference from the time starting of austenite formation to the time reaching a given volume of

austenite fraction (fA = 10% to 50%). For example, ∆t'Ac1-50% represents the time increment from

the time at temperature Ac1 to the time when fA reaches 50%. The slopes of trend lines are

negative, which reveals that the transformation time for a certain volume fraction of austenite

decreases with increasing heating rate. The absolute value of a slope decreases with the

increment of austenite volume fraction, which indicates that the effect on transformation time is

weakened as the transformation proceeds.

The linear features shown in Figure 5.6 (a) and (b) provide useful information for modeling

austenite formation. Nucleation and growth are the two main mechanisms operating in the phase

transformation process. Their rates can be modelled using the equations of [42, 101, 105, 115,

119, 137]:

0 exp( ) NQN N

RT (5.6)

0 exp( ) GQG G

RT (5.7)

where R is the gas constant, T is the absolute temperature; QN and QG are activation energy of

nucleation and growth, respectively; N0 and G0 are pre-exponential factors which can be

functions representing the effects of influencing factors on nucleation and growth. With respect

to the formula of N0 and G0, in addition to the material related parameters, heating rate as a

critical thermodynamic factor should also be taken into account in non-isothermal austenite

formation. According to the results obtained in this work, it is suggested that it should be

integrated in terms of a power law.

97

5.2.3.2 Effects of heating rate on isothermal austenite formation

Figure 5.7 shows the required time to increase austenite volume fraction by 5% from different

stages (fA = 80%, 85%, and 90%) of the isothermal transformation for different heating rates. The

isothermal transformation takes place at a constant soaking temperature of 1173K, at which full

austenite formation is achievable. In the Figure, Δt, which is termed as soaking time increment,

represents the time difference from the time corresponding to a certain austenite volume fraction

(fA) to the time reaching another higher value of fA during soaking. For example, Δt80%-85%

represents the time increment from the time when fA is 80% to the time when fA reaches 85%. It

can be seen, again, that the relationship of heating rate and soaking time increment is linear,

when plotted on log-log scales. Similar to Figure 5.6 (b), the slopes of trend lines are negative.

This reveals that, for the same stage of transformation, under the same isothermal condition, less

time is required for a higher heating rate. This leads to an important conclusion that the

thermodynamic effect of heating rate proceeds from the heating-up step and continues through

the subsequent isothermal soaking step. This is because the transformation rate at any time

depends on both the instant growth rate of new phase grains and the existing quantity of the

grains (not only on instantaneous nucleation rate) [119]. During continuous heating, a higher

heating rate stimulates a higher nucleation rate, which allows more nuclei used for austenite

formation to be generated even within a shorter period [109]. Therefore, during subsequent

isothermal soaking at a given temperature, a larger amount of pre-existing grains enables higher

overall growth rate of new phase, that is, a higher austenite formation rate. It can be observed that

all the trend lines in Figure 5.7 are nearly parallel. This interesting feature indicates that the

influence of heating rate on the isothermal transformation remains constant throughout different

austenite formation stages. Moreover, another feature shown in Figure 5.7 is that longer time is

required to increase austenite volume fraction by 5% at a later stage of transformation, which

reveals the impingement mechanism in the steel [119].

98

Figure 5.7 Effects of heating rate on the transformation time to increase austenite volume fraction

by 5% from 80%, 85% and 90% during soaking at 1173K

The evolution curves of austenite volume fraction, corresponding to a period of 10 minutes

starting from isothermal soaking, for each of the three testing conditions, are plotted on the base

of normalised time in Figure 5.8. Regarding Figure 5.8 (a), for each heating rate, the time for fA =

80% is taken as the origin of the horizontal axis, the soaking time increment ∆t80%–85% is taken as

a unit for time normalization. The normalised time is given by (t-t80%)/∆t80%–85%, where t is the

instant time at a time scale starting from the time at temperature of 873K, t80% is the time for fA =

80% for the same time scale, ∆t80%–85% is the transformation time to increase austenite volume

fraction by 5% from 80%. The condition for this normalization is the influence of temperature

and heating rate being constant throughout the interested progress. With time normalization, the

feature of an evolution curve should be determined only by metallurgical properties which

control the transformation kinetics. Its dependency on temperature and heating rate has been

eliminated automatically. As shown in Figure 5.8 (a), the evolution of austenite volume fraction,

with normalised time with the starting point of fA = 80%, for all heating rates lies on a same curve

10

100

1000

1 10 100

Soak

ing t

ime

incr

emen

t, Δ

t (s

)

Heating rate, (K/s)

99

and slows towards a volume fraction of 100%. This indicates that the impingement mechanism

under the isothermal transformation stage does not depend on heating-up conditions in the

considered range. Moreover, the figure shows a comparison of austenite formation progress for

different heating rates. For example, the curve for the highest heating rate, 25K/s, even starting

with the lowest volume fraction of austenite, is the one that most approximates to equilibrium

after the same transformation time. This once again shows that a higher heating rate enables a

higher rate of subsequent isothermal transformation in the studied steel. In Figures 5.8 (b) and (c),

the time for fA = 85% and 90% is taken as the origin of the horizontal-axis respectively, and is

normalised by soaking time increments Δt85%–90% and Δt90%–95%, respectively, which is similar to

the horizontal axis in Figure 5.8 (a). The same features shown in Figure 5.8 (a) can be found in

figures 5.8 (b) and (c). The only difference of the three figures is the normalised time scale, since

the value of ∆t (normalised) becomes higher at the later stage of the transformation as shown in

Figure 5.7. Figure 5.8 indicates that the effect of heating rate on austenite formation can be

eliminated if the transformation time is normalised using the method introduced here.

100

(a) Normalised by Δt80%–85%

(b) Normalised by Δt85%–90%

(c) Normalised by Δt90%–95%

Figure 5.8 Volume fractions of austenite for different heating rates with time normalised by the

soaking time increments for different austenite volume fractions, during soaking at 1173K

0%

20%

40%

60%

80%

100%

-4 -2 0 2 4 6 8 10 12 14 16 18 20 22

Vo

lum

e f

ra

cti

on

of

au

sten

ite, f A

Normalised time, (t-t80%)/Δt80%−85%

25K/s

5K/s

1K/s

0%

20%

40%

60%

80%

100%

-4 -2 0 2 4 6 8 10 12

Vo

lum

e f

ra

cti

on

of

au

sten

ite, f A


25K/s

5K/s

1K/s

0%

20%

40%

60%

80%

100%

-2 0 2 4 6

Volu

me f

ra

cti

on

of

au

sten

ite, f A


25K/s

5K/s

1K/s

101

5.2.4 Analysis of intercritical annealing

In the second group of tests, the specimens were heated at the same rate of 5K/s to different

temperatures (1023K, 1073K, 1123K and 1173K), and then kept at these individual temperatures

for a sufficient period (15 minutes in this work) to enable an equilibrium condition of austenite

formation to be achieved at each temperature. This provides insight into the kinetics of austenite

formation during isothermal soaking at intercritical temperatures.

5.2.4.1 Saturated volume fraction

Figure 5.9 Saturated volume fractions of austenite at different soaking temperatures

If the steel is soaked at an intercritical temperature between Ae1 and Ae3, shown in Figure 5.1, the

volume fraction of transformed austenite can never reach 100% [99, 104]. In this work, the value

of austenite volume fraction that can ultimately be achieved at any given soaking temperature, T,

is known as saturated volume fraction fAs [99, 104]. Referencing the austenite formation and

saturation features shown in Figure 5.4 (b), the saturated austenite volume fraction fAs for

different soaking temperatures (between Ae1 and Ae3, or above Ae3) can be obtained and are shown

in Figure 5.9.The experimental results show a typical S-type of relationship on fAs-T axes. The

0%

20%

40%

60%

80%

100%

600 650 700 750 800 850 900 950 1000

Satu

rate

d v

olu

me

fra

ctio

n o

f

au

sten

ite,

fs

Temperature (K)

873 923 973 1023 1073 1123 1173 1223 1273

Ae1 Ae3

102

reference Ae1 and Ae3 for the type of studied steel provided by alloy supplier are 993K and 1118K,

respectively. However, these values have tolerances since the chemical composition and starting

microstructure of the alloy may vary from batch to batch. The result obtained in this study is

slightly different from the reference: when soaking temperature is 1123K, fAs is 92%, which is

acceptable for the study. Therefore, in this study, Ae3 is taken as a temperature between 1123K

and 1173K.

According to the analysis in subsection 5.2.3, it is also known that, although heating rate affects

the austenite formation rate, it does not affect the maximum obtainable value of austenite fraction

at a given soaking temperature, i.e. fAs is a function of only temperature.

5.2.4.2 Effects of temperature on isothermal austenite formation

Figure 5.10 shows the transformation time to increase austenite volume fraction by 10% of fAs

from 80% of fAs (i.e. fA = 80%fAs–90%fAs) for different soaking temperatures. Again, Δt is the

soaking time increment, Δt80% fAs-90% fAs represents the time increment from the time when fA is 80%

of fAs to the time when fA reaches 90% of fAs. It can be seen that less transformation time is

required at a higher temperature; in addition, the relationship between logarithmic soaking time

increment, ln(Δt), and inverse temperature, 1/T, approximately follows a straight line, which can

be given by:

exp( ) CQt C

RT (5.8)

where C is a material constant, Qc activation energy, R the gas constant, and T absolute

temperature. The regularity can be explained as follows: In the studied steel, it can be expected

that the nucleation of austenite occurs only in pearlite colonies and all the nucleation sites are

consumed quickly at the beginning of the transformation [42, 96, 109]. Thus, having the same

heating rate, same amount of nuclei is supposed to be generated in the tests. Then, the

103

transformation rate is controlled by only the growth rate of the austenite phase. Thus, it is

determined by only the soaking temperature under isothermal conditions. This is the reason that,

considering transformation time and rate are in inverse proportion, the formula (5.8) is consistent

with equation (5.7).

Figure 5.10 Effects of soaking temperature on the transformation time to increase austenite

volume fraction by 10% of fAs from 80% of fAs

The evolution curves of austenite volume fraction, corresponding to a period of 10 minutes

starting from 80% of fAs for each of the four soaking temperatures, are plotted on the base of

normalised time in Figure 5.11 (a). For each test, the time for fA = 80% fAs is taken as the origin of

horizontal axis, the soaking time increment 80%fAs(T)–90%fAs(T) is taken as a unit for time

normalization. Thus the normalised time can be given as (t-t80%fAs)/∆t80%fAs–90%fAs. In the figure,

the different progressing rates of austenite formation within a same time period are illustrated.

This again indicates that higher soaking temperature enables faster transformation progress

towards equilibrium.

Δt80%fAs–90%fAs = 0.067exp(8604/T)

10

100

1000

8.5E-04 9.0E-04 9.5E-04 1.0E-03

So

ak

ing t

ime i

ncrem

en

t, Δ

t (s

)

Inverse Temperature, 1/T (1/K)

1173K 1123K

1073K

1023K

104

In Figure 5.11 (b), the same horizontal axis as Figure 5.11 (a) is employed. For the vertical axis

the austenite volume fraction, shown in Figure 5.11 (a), is normalised by fAs of the corresponding

soaking temperature. Similar to Figure 5.8, it is seen that the trends of curves are almost identical,

which reveals that the isothermal austenite formation at different intercritical temperatures obeys

the same kinetics of growth and impingement approaching equilibrium.

(a) Time is normalised by Δt80%fAs–90%fAs

(b) Time is normalised by Δt80%fAs–90%fAs and volume fraction of austenite is normalised by fAs

Figure 5.11 Evolution curves of austenite volume fraction for different temperatures under

isothermal transformation conditions

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6

Vo

lum

e f

ra

cti

on

of

au

sten

ite,

fA

Normalised time, (t-t80%fAs)/Δt80%fAs−90%fAs

1173K

1123K 1073K

1023K

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6

Norm

ali

zed

vo

um

e f

ra

cti

on

of

au

sten

ite, f A

/fA

s

Normalised time, (t-t80%fAs)/Δt80%fAs−90%fAs

1173K

1123K

1073K

1023K

105

5.3 Thermo-mechanical properties of boron steels under hot stamping conditions

The flow stress-strain relationships of the austenite and initial phase of boron steel under hot

stamping conditions are obtained from hot tensile test data. To improve accuracy of results, the

test data corresponding to necking stage is corrected using a method described in Appendix 2; in

addition, the real strain rate for each test is evaluated, as suggested in Chapter 4 (subsection

4.3.2.3). Based on the results, the effects of strain rate and temperature on the deformation

behaviours of boron steel in the both phase states are characterised.

5.3.1 Results: flow stress-strain curves

5.3.1.1 Strain rate and temperature dependence of austenite

Strain rate dependence

Figure 5.12 Experimental flow stress-strain relationships for austenite for different strain rates at

a deformation temperature of 973K

The strain rate dependence of the tensile behaviour of boron steel in the austenitic state has been

investigated for a deformation temperature of 973K. Figure 5.12 shows a set of true stress-strain

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5

Tru

e s

tress

(M

Pa

)

True strain

2.45/s

0.40/s

0.045/s

0.006/s

106

curves for different strain rates (the real values of true strain rates are 0.006/s, 0.045/s, 0.40/s, and

2.45/s). The peak flow stress is higher for a higher strain rate, which indicates the viscoplastic

nature of material under the test conditions.

For viscoplastic solids at elevated temperatures, the pure elastic deformation is quite small and

the initial yield stress is difficult to determine [138], thus analysis of this experimental data

focuses on the plastic deformation. At the initial stage of plastic deformation, the steep increase

of flow stress is mainly attributed to the viscous stress, which is strain rate dependent. Since

initial yield strength is a function of temperature [138], the values of it should be the same for

this group of flow curves due to the same deformation temperature. Thus, the fact that flow stress

levels for different strain rates vary little at a small deformation (true strain εT < 0.005) may

suggest that the strain rate sensitivity of viscous stress for the austenite of boron steel is relatively

low. Subsequently, the gradual increase of flow stress with increasing strain is mainly related to

work hardening, caused by dislocation accumulation and interactions [138]. Concurrently, the

increasing trend is slowed down due to dynamic and static recovery processes, through

annihilation of dislocations and relaxation of internal stresses [62]. Since static recovery is a

function of time [62], for a lower strain rate, dislocation density is more reduced so that apparent

hardening is not as great as that for higher strain rates, which is clearly manifested in the trend of

flow curves in the figure. Significant variations in the hardening exponent for different strain

rates can indicate that the static recovery for the material at the tested temperature is pronounced.

The plateau of flow curves reveals the achievement of a steady state between strain hardening

and recovery [57]. Larger extended ductility after the peak flow stress can be seen for a lower

strain rate. Towards the end of deformation the softening mechanism of micro-damage dominates

deformation [139], which is reflected by the dramatic drop of flow stress.

107

Temperature dependence

Figure 5.13 Experimental flow stress-strain relationships for austenite for different deformation

temperatures (designed strain rate: 0.50/s)

The temperature dependence of the tensile behaviour of austenite has been investigated for a

designed strain rate of 0.50/s, which is a typical rate that the material is subjected to in hot

stamping practice. Figure 5.13 shows a set of true stress– strain curves for different deformation

temperatures of 873K, 973K, and 1073K. The real strain rates for each test are: 873K-0.30/s,

973K-0.40/s, 1073K-0.50/s. The variations are negligible for the analysis here. Strong

temperature sensitivity of the material is revealed by the curves: with increasing temperature

resulting in significant reduction of initial strain hardening and peak flow stress, as well as

increase of ductility. The result is typical of most metals, in which deformation associated

processes are thermally activated. For a higher temperature, dislocation mobility is higher due to

increased thermal vibration of the lattice and decreased strength of obstacles to dislocation

movement, thus lower flow stress is required to facilitate further straining [140]. In addition,

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5

Tru

e s

tress

(M

Pa

)

True strain

873K

973K

1073K

108

grain-boundary sliding and rotation, as well as microstructural recovery are more activated with

the increasing temperature [141], which enables larger ductility.

5.3.1.2 Strain rate and temperature dependence of initial phase

Strain rate dependence

Figure 5.14 Experimental flow stress-strain relationships of the initial phase for different strain

rates at a deformation temperature of 923 K

The influence of strain rate on the tensile behaviour of boron steel in the initial phase state has

been investigated for a deformation temperature of 923K. Figure 5.14 illustrates the

viscoplasticity of the alloy through a group of true stress-strain curves for strain rates of 0.01/s,

0.10/s, 0.70/s, and 3.20/s. A large increase in flow stress level with the increasing strain rate is

shown at a small plastic deformation (εT < 0.005), which reveals significant strain rate sensitivity

of viscous stress for the initial phase of boron steel. For higher strains, flow stress keeps

increasing gently for all strain rates, until the damage mechanism becomes dominant. Fracture

takes place at almost the same strain level regardless of that value of strain rate. These features

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5 0.6

Tru

e t

ress

(M

Pa

)

True strain

3.20/s 0.70/s

0.10/s

0.01/s

109

suggest that microstructural recovery may not be pronounced for the initial phase of boron steel

at the tested temperature.

Temperature dependence

Figure 5.15 Experimental flow stress-strain relationships of the initial phase for different

deformation temperatures (designed strain rate: 0.50/s)

The influence of temperature on the tensile behaviour of the initial phase has been investigated

for a designed strain rate of 0.50/s. Figure 5.15 shows a group of true stress-strain curves for

different deformation temperatures of 723K, 823K, and 923K. The real strain rates for each test

are: 723K-0.35/s, 823K-0.50/s, 923K-0.70/s. The variations are negligible for the analysis.

Similar to the curves for austenite in Figure 5.13, a lower strain hardening and peak flow stress

level, but greater ductility, can be seen for a higher deformation temperature.

5.3.2 Characterisation of flow stress response

Further analysis has been carried out to quantify the effects of strain rate and temperature on the

flow stress response of both phase states, which can provide necessary information for material

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6

Tru

e s

tress

(M

Pa

)

True strain

723K

823K

923K

110

modelling. Moreover, the influence of flow stress features on deformation uniformity is

discussed.

5.3.2.1 Effects of strain rate

Since a uniform thickness reduction is desired in hot stamped panels for automotive applications,

deformations during forming normally correspond to low strains before the peak stress is

achieved. The features of stress response during the hardening stage are critical to the

deformation mode of the alloy. Flow stress at strain levels of 0.005, 0.05, and 0.1 are chosen for

analysis in this study.

Figure 5.16 summarises stress values at the three strain levels for various strain rates: the

subfigure (a) is for austenite tested at a temperature of 973K, and (b) is for the initial phase tested

at 923K. By plotting logarithmic stress against logarithmic strain rate, linear fits have been

obtained, which suggests the power law viscoplastic response of both phase states.

In both sub Figures 5.16 (a) and (b), for any strain rate, the stress increments with increasing

strain level reveal the strain hardening characteristic; with respect to any strain level, the increase

of stress with increasing strain rate exhibits the strain rate hardening characteristic. The strain rate

hardening exponent is represented by the slope of trend lines, m', and corresponds to the power

exponent in the equations. For example, in subfigure (a), m' is 0.062 at 𝜀𝑇 = 0.005 and increases

to 0.107 at εT = 0.1. It is a critical factor influencing the uniformity of deformation during

forming processes. Generally, a larger m' value indicates a higher tendency to reduce the strain

rate gradient within the material flow. When m' changes with strain, the flow condition is

complex and the consideration of the trend of m' is important. For instance, austenite has a

smaller m' value at εT = 0.005 compared with the initial phase, but larger m' increments for

subsequent straining (from 0.005 to 0.05 and from 0.05 to 0.1). In this case, the locally larger

deformation, which is deformed at a relatively greater strain rate, can be strongly impeded from

111

further developing. Therefore, for the two phase states deformed at their respective temperatures,

there is possibility for austenite to achieve better deformation uniformity.

(a) Austenite tested at 973K, strain rates: 0.006/s, 0.045/s, 0.40/s, and 2.45/s

(b) Initial phase tested at 923K, strain rates: 0.01/s, 0.10/s, 0.70/s, and 3.20/s

Figure 5.16 Flow stress at different strain levels (0.005, 0.05, and 0.1) for different strain rates

50

0.001 0.01 0.1 1 10

Tru

e s

tress

(M

Pa

)

True strain rate (/s)

100

200

400

300

m'

100

0.01 0.1 1 10

Tru

e s

tres

(MP

a)


400

200

m'

112

5.3.2.2 Effects of temperature

Figure 5.17 summarises the flow stress values at true strain levels of 0.005, 0.05, and 0.1 for

different deformation temperatures at the same designed strain rate of 0.50/s: the subfigure (a) is

for austenite tested at temperatures of 873K, 973K, and 1073K; (b) is for the initial phase tested

at 723K, 823K, and 923K. By plotting logarithmic stress against inverse temperature, the linear

fit in subfigure (a) indicates that the temperature dependence of flow stress for austenite follows

the standard Arrhenius activation energy equation; however, small deviations from linearity are

observed for the initial phase in subfigure (b).

As can be seen, at strain levels of 0.05 and 0.1, the flow stress gradients with temperature are

more pronounced for ferrite deformed in the temperature region (723K–923K) than austenite

deformed between 873K–1073K. It suggests that the austenite is more likely to be deformed

uniformly under selective heating and press hardening conditions.

(a) Austenite (b) Initial phase

Figure 5.17 Flow stress at different strain levels (0.005, 0.05, and 0.1) for different deformation

temperatures (designed strain rate: 0.50/s)

100

9.0E-04 1.0E-03 1.1E-03 1.2E-03

Tru

e s

tress

(M

Pa

)


300

400

200

1073K

973K

873K

100

1.0E-031.1E-031.2E-031.3E-031.4E-03

Tru

e s

tres

(MP

a)


923K

300

923K

823K

723K

500

600

400

200

113

5.4 Mechanical properties of boron steels at room temperature

The flow stress-strain relationships for boron steel having various microstructures are obtained

from tensile tests at room temperature. First, the dynamic tensile behaviour of martensite and

initial phase over a wide of strain rates (up to 500/s) is discussed. Second, the mechanical

properties of boron steels over a series of phase compositions (martensite volume fraction: fM = 0%

to 100%) are characterised.

5.4.1 Dynamic tensile behaviour of the martensite and initial phase for boron steel

5.4.1.1 Results: flow stress-strain curves

The true stress-strain relationships of martensite and initial phase (ferrite and pearlite) for strain

rate ranging from 0.001/s to 500/s have been achieved. Representative curves for each phase state

are shown in Figure 5.18, where data for the high testing rate have been smoothed. It is well-

known that martensite is a hard and brittle phase, while ferrite is soft and ductile and this is well

manifested in the figure. For the same strain rate of 0.001/s, the true ultimate tensile strength

(σUTS) values are 1499MPa and 620MPa for the martensite and initial phase respectively; while

the elongations are 0.1 and 0.163. Here, σUTS refers to the true stress when the material is

subjected to maximum tensile loading; elongation refers to the true strain at failure.

114

(a) Martensite (fM = 100%)

(a) Initial phase (fM = 0%)

Figure 5.18 True stress-strain curves of the martensite and initial phase of boron steels for

different strain rates tested at room temperature

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1 0.12

Tru

e s

tress

(M

Pa

)

True strain

500/s

200/s

5/s

0.001/s

0

100

200

300

400

500

600

700

800

900

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Tru

e s

tress

(M

Pa

)

True strain

200/s

50/s

5/s

0.001/s

115

Over the large range of strain rate, viscoplastic properties are observed for both phase states.

Both exhibit continuous-yielding at all strain rates for the cold deformations, no upper and lower

yield point or yield point elongation can be seen. By comparison, the initial phase has a little

higher viscosity and the martensite has stronger work hardening. No static recovery is expected

to take place at room temperature [142], thus the increasing trend of flow curves could be the

result of simultaneous dislocation hardening and dynamic recovery. For martensite, at all values

of strain rate, the flow stress reaches a peak at about half elongation. For ferrite, at all values of

strain rate, flow stress increases nearly until fracture. This feature further reveals the advantage of

the initial phase in enhancing ductility. It is also consistent with the typical ductile facture mode

that damage accumulation evolves little at lower strain levels but continues at a rapid rate

immediately prior to fracture [143]. For both phase states, the reduction of ductility with

increasing strain rate can hardly be seen. This would benefit the performance of the alloy during

impact.

5.4.1.2 Strain rate sensitivity of the phase states

To rationalise the strain rate sensitivity of the alloy, the trends in true ultimate tensile strength

and elongation, as a function of true strain rate are examined in Figure 5.19 (a) and (b),

respectively. By plotting logarithmic true ultimate tensile strength (σUTS) and elongation (εf)

against logarithmic true strain rate (εT), linear fits are obtained, which accords with the power law

viscoplastic response of both phase states. The strain rate hardening exponent (same as the

definition in Figure 5.16) is found to be 0.012 for martensite and 0.022 for initial phase, which

respectively corresponds to about 13% and 23% increase in the σUTS over 5 orders of magnitude

change in strain rate. The ductility in both phase states exhibits very modest strain-rate sensitivity.

In general, the initial phase shows more pronounced strain rate dependence, which is consistent

with the theory that the strain rate sensitivity decreases with increasing strength level [144].

116

(a) Effects of εT on true UTS (σUTS) (b) Effects of εT on elongation (εf)

Figure 5.19 Effects of strain rate (0.001/s, 0.05/s, 5/s, 50/s, 200/s, and 500/s) on the tensile

properties of the martensite and initial phase of the boron steel

5.4.2 Effects of microstructure on tensile behaviour of boron steel

5.4.2.1 Relationships between mechanical properties and phase composition

The values of true ultimate tensile strength (σUTS) under quasi-static testing, hardness (h), and

martensite volume fraction (fM) for representative samples having various phase compositions are

summarised in Figure 5.20. The straight trend lines in the figure indicate that any two of the

parameters are directly proportional to each other. With the increase of fM in the boron steel, its

strength and hardness increase. The reason to plot σUTS and fM as a function of h is that, by

adopting their relations, the mechanical-property/microstructural distribution in an as-formed

boron steel panel can be easily evaluated by hardness measurement.

100

1000

0.001 0.01 0.1 1 10 100 1000

Tru

e u

ltim

ate

ten

sile

str

en

gth

(M

Pa

)


Martensite

Initial phase

500

0.01

0.1

0.001 0.01 0.1 1 10 100 1000

Elo

ng

ati

on


Martensite

Initial phase

0.5

0.05

117

In this study, hardness (h) for full martensite and initial phase (78% proeutectoid ferrite and 22%

pearlite) are 473HV and 173HV, respectively; when h is between about 285HV and 473HV, the

steel is composed of proeutectoid ferrite and martensite; when h is between about 230HV and

285HV, the steel comprises proeutectoid ferrite, martensite, and a small amount of bainite; when

h is between about 173HV and 230HV, a ferrite matrix with dispersions of pearlite, bainite and

martensite phases, exists. Based on the relationships obtained in the figure, it is reasonable to

simplify the multiphase boron steel as dual-phase of ferrite and martensite, and interpolate the

value of fM as the equivalent martensite volume fraction according to the hardness value for the

range, 173HV–285HV.

Figure 5.20 The relationships of true ultimate tensile strength and martensite volume fraction

with hardness for heat treated boron steel with various phase compositions

5.4.2.2 Effects of phase composition on tensile properties

Figure 5.21 shows a series of representative true stress-strain curves. The volume fraction of

martensite (fM) measured for each phase state is marked on the corresponding curve. All curves

σUTS = 2.77h + 225.7

0%

20%

40%

60%

80%

100%

0

200

400

600

800

1000

1200

1400

1600

1800

100 200 300 400 500

Tru

e u

ltim

ate

ten

sile

str

en

gth

, σ

UT

S

(MP

a)

Hardness, h (HV30)

Vo

lum

e f

ra

cti

on

of

ma

rte

nsi

te,

f M

fM =0.0032h-0.55

118

exhibit continuous yielding. With the increasing volume fraction of martensite, the flow stress

level increases, and the ductility dramatically decreases first for fM = 0%–61.3%. Ductility for fM

= 61.3% and 88.5% is less than that for full martensite.

Figure 5.21 True stress-strain curves of heat treated boron steel with various volume fractions of

martensite (quasi-static tests for the strain rate of 0.001/s at room temperature)

To further investigate the effects of phase composition on the tensile properties of boron steel,

experimental values of true ultimate tensile strength (σUTS ), 0.2% proof stress (σ0.2% ) and

elongation (εf), for all phase states, are plotted against the volume fraction of martensite (fM) in

Figure 5.22. The values of fM for part of specimens without microstructural observation are

calculated from their hardness values. Generally, the plastic behaviour (hardening and damage)

of multiphase steels is governed by both phase composition in volume fraction and

morphological distribution of the phases [145]. For example, several characteristics of the

martensite phase have been shown to affect the degree of void damage development including:

volume fraction, distribution, grain size, etc. [146, 147]. With respect to this work, since boron

steel with different phase states are heat treated from the same initial microstructure, and

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Tru

e s

tress

(M

Pa)

True strain

0%

100%

88.5%

61.3%

42.1%

119

subjected to the heating rate and soaking time, variations in morphological factors can be

neglected [148]. Therefore, it is reasonable to characterise the tensile properties of the studied

boron steels only as a function of fM.

Figure 5.22 Effects of martensite volume fraction on tensile properties of heat treated boron

steels (quasi-static tests for the strain rate of 0.001/s at room temperature)

As shown in Figure 5.22, stress level increases with increasing fM due to the strengthening of

hard phase martensite. The relationship between 𝜎𝑈𝑇𝑆 and fM follows a linear fit, which has been

presented in Figure 5.20. Interestingly, the relationship between 0.2% proof stress and fM is found

to follow an exponential fit better than a linear fit, which reveals the value of 0.2% proof stress

for a multiphase composition is lower than the value expected for a linear fit. This might be

explained as: for the multi-phase steels quenched from intercritical temperatures, as austenite is

transformed to martensite during quenching, dislocations are formed in the ferrite phase to

accommodate the shear deformation and volume expansion associated with the martensitic

σUTS = 867fM + 692

σ0.2% = 271exp(1.25fM)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0

200

400

600

800

1000

1200

1400

1600

1800

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Str

en

th (

MP

a)

Volume fraction of martensite, fM

True UTS

0.2% Proof stress

Elongation

Elo

ng

ati

on

E

lon

ga

tio

n

Elo

ng

ati

on

E

lon

ga

tio

n

120

transformation [149]. These highly mobile dislocations are responsible for the low yield strength

and continuous yield behaviour [150].

The trend of elongation with martensite volume fraction is more complex: for fM between about

0%–60%, an inversely proportional trend between elongation and fM can be found; for fM between

about 60%–95%, apparent reductions in elongation are observed; for fM higher than 95%, the

values of elongation are almost identical. The poor ductility of dual phase boron steel

corresponding to fM = 60%–95% is noteworthy, for which the possible reason is proposed: if steel

comprised of multiple phases is subjected to tension, stress concentrations and strain

incompatibilities will arise, due to the interactions of different phases having different tensile

properties. The mechanism of failure was found to be influenced by deformation localization due

to microstructural inhomogeneity [151]. And the second phase can be treated as inhomogeneous

inclusions embedded in a matrix [152]. For the studied steel, since pure ferrite and martensite

phases have greatly different stress-strain behaviour, voids can be generated between the ferrite

boundaries triggered by deformation mismatch with adjacent martensite particles or local stress

concentrations, or at intersections of different phases initiated by negative internal pressure [143,

151]. This suggests that more voids are apt to be generated if there are more phase interfaces [31],

which enhances damage development.

5.5 Summary

The effects of heating rate and temperature on austenite formation under both isothermal and

non-isothermal conditions have been characterised. Rational understanding of the mechanisms

which control the austenite formation in the boron steel has been obtained. The mechanisms

involved in the deformation of the austenite and initial phase at elevated temperatures have been

analysed; at the same time, the effects of strain rate and temperature on the deformation

behaviour of the boron steel have been rationalised. The viscoplastic behaviour of the martensite

121

and initial phase subjected to high strain rate at room temperature has been observed and

characterised; in addition, the empirical relations between mechanical properties (True ultimate

tensile strength, 0.2% proof stress, elongation, and hardness) and phase compositions (volume

fraction of martensite), for boron steel with various microstructures, have been summarised. The

results and conclusions achieved in this chapter will be used for materials modelling in the next

chapter.

122

CHAPTER 6 MATERIALS MODELLING

6.1 Introduction

In this chapter, following the tests and result analysis in Chapter 4 and Chapter 5, three sets of

physically-based material models are defined: an austenite formation model for the boron steel

during selective heating, and two viscoplastic-damage constitutive models respectively for boron

steels under hot stamping conditions and in crash scenarios. Based on insight into microscopic

mechanisms which act to cause the material changes, phenomenological approaches are adopted

by modelling processes to capture the dominant features of phase transformation and mechanical

response of boron steels at the macroscopic level.

6.2 Development of austenite formation model for the boron steel during

selective heating

A physically-based material model is developed to describe the austenite formation in the boron

steel during selective heating in hot stamping processes. The equations are formulated based on

three austenite formation mechanisms: nucleation, growth and impingement. The evolution rate

of state variables, such as extended volume, saturated volume fraction, and real volume fraction

of austenite, are modelled. The data from heat treatment experiments are used to calibrate and

validate the equations. Further analysis is made to illustrate the significance of the model in

applications.

123

6.2.1 Model development

6.2.1.1 Extended volume of austenite

At the first step of the modelling, the equations will involve the calculation of extended volume

of growing austenite phase. The definition of extended volume is based on a hypothesis assuming

that nucleation and growth apply to an infinite volume of untransformed material, where every

single nucleus is unaffected by the formation and growth of other nuclei [118, 119]. For this

situation, the development of equations for nucleation and growth of austenite is described below.

In classic theory, nucleation rate is defined as the number of nuclei (particles of supercritical size)

formed per unit volume, per unit time [96, 119]. It is determined by the number of particles of

critical size and the rate of the jumping of atoms through the interface between initial phase and

particles of critical size. For large overheating conditions, the nucleation rate of austenite can be

formulated in the Arrhenius term [119, 153]:

0 exp NQN N

RT

(6.1)

where R is the gas constant, T is the absolute temperature, QN is the activation energy for the

jumping of atoms through the interface, and N0 is the pre-exponential factor. This equation

describes a nucleation mode of constant rate at a constant temperature without pre-existing nuclei

(i.e. when t = 0, the number of nuclei: N = 0). Both QN and N0 are temperature and time

independent.

With respect to the pre-exponential factor N0, it can be formulated by characterizing the effects of

influencing factors on the austenite formation. The internal influencing factors are related to the

starting microstructure of the material, and the external ones are related to heating rate and

temperature. For austenite nucleation in pearlite, Roosz et al. have investigated its dependence on

124

material structure [43, 101, 105, 113]. N0 was proposed as a morphological function of

interlamellar spacing (λ), the edge length of pearlite colony (αp), and the number of nucleation

sites (NC):

0 ( , , )p

CN f a N (6.2)

Furthermore, Caballero et al. [43, 101, 105, 113] extended the applications to non-isothermal

conditions by adding the effects of heating rate (T) into function (6.2):

0 ( , , , )p

CN f a N T (6.3)

In this study, because the model is specialized for a particular steel, the morphological

parameters in equations (6.2) and (6.3) can simply be merged. The influence of heating rate on

nucleation was suggested to be taken into account in terms of a power law, according to the

analysis in the previous chapter. Thus, the nucleation rate can be modelled using:

0 1 exp ( )

0 ( )

A NA P

A P

QN A AT f f

RT

f f

(6.4)

where QN is the activation energy for nucleation, R is the gas constant, T is heating rate; A0, A1,

and φA are constants characterizing the overall effects of internal and external influencing factors;

fA is the transformed volume fraction of austenite, and fP is the initial volume fraction of pearlite.

The austenite formation in the studied steel is via two routes: transformation from pearlite to

austenite and from pro-eutectoid ferrite to austenite. It is expected that nucleation of austenite

occurs only in pearlite colonies at the beginning of the transformation [42, 96, 109]. Thus

equation (6.4) defines continuous nucleation and site saturation modes for the first and second

step of the austenite formation, respectively. When dissolution of pearlite has finished (fA > fP),

the saturation of nucleation sites causes a zero nucleation rate for the austenite-ferrite

125

transformation [119]. The first term in equation (6.4) represents static nucleation of austenite, and,

the second is related to the dynamic effect of heating on austenite nucleation for fA ≤ fP.

Similar to the formulation of nucleation rate, the volume growth rate of a nucleus (��) is proposed

in the Arrhenius term:

0 exp vQv v

RT

(6.5)

where, Qv is the activation energy for the volume growth, and v0 is the pre-exponential factor.

Analytically, Qv is a function of the activation energy for the front migration (Qm), the growth

mode parameter (m), and the dimensionality of the growth (d) [118, 119]:

( , , )v mQ f Q m d (6.6)

At the same time, the pre-exponent factor v0 is given as [118, 119]:

0 ( , )v f g (6.7)

where g is a particle-geometry factor, η is a growth factor determined by solute concentrations of

the transformed and initial phases. Depending on the growth mode (interface controlled growth,

volume diffusion controlled growth, or mixed-mode growth), the functions (6.6) and (6.7) can be

formulated as various equations of great complexity.

Considering the trade-off between modelling comprehensiveness and mathematical simplicity,

for the particular steel in this study, a straight forward equation to describe the volume growth

rate of an austenite particle is proposed as:

0 1 expB vQv B B T

RT

(6.8)

126

where Qv is the activation energy for volume growth independent of temperature and time; B0, B1,

and φB are material constants to be determined from experimental data. Qv, B0, B1, and φ

B can be

piecewise constants if the growth mode changes during transformation.

Assuming that all austenite nuclei grow at the same rate under same heating conditions, the

growth rate of the extended volume of austenite (Ve ), in a unit of real sample volume, can be

calculated by:

eV Nv (6.9)

Equation (6.9) expresses that the extended volume growth rate at any time is determined by both

the existing quantity of formed nuclei and the instant growth rate of the nuclei.

6.2.1.2 Real volume fraction of austenite

Normally, since there is more than one nucleus growing during transformation, the extended

volume of transformed phase should be correlated to real volume by taking impingement into

account. The widely used model proposed by Avrami [96] is presented below:

1 exp( )A Af f (6.10)

where fA is the real volume fraction of transformed phase, and f

A

' is the extended volume fraction

which represents the extended volume of transformed phase in a unit of real sample volume

(equivalent to Ve in this study). The interpretation of equation (6.10) can be made based on its

differential form:

(1 )A AA

df dff

dt dt

(6.11)

127

For a time increment dt, the extended volume fraction increment of transformed phase is dfA

', but

only part (as large as the untransformed volume fraction (1–fA) will contribute to the change of

real volume fraction dfA [119].

This classical theory well accounts for the overlap of growing particles (hard impingement), but

equations (6.10) and (6.11) are restricted to the case of hard impingement with all nuclei

randomly dispersed [119]. With respect to diffusion controlled transformations, the

transformation rate slows down when diffusion fields surrounding the new phase particles start to

overlap [118, 119]. This mode is denoted as soft impingement [96, 118, 119], which deviates

from the JMA kinetics mentioned above. In order to adapt the theory to complex nucleation and

growth modes, appropriate adjustments of the formulation are necessary.

Therefore, for the purpose of correlation, an equation extended from equation (6.11) to describe

the real volume fraction of austenite in this study is proposed as:

1(1 )

m eA A n

e

Vf f

V

(6.12)

where fA

is the real volume fraction of austenite, fA is the rate of f

A with time; Ve, as

aforementioned, is the extended volume of austenite in a unit of real sample volume which is

equivalent to fA

', in equations (6.10) and (6.11), Ve is the rate of Ve. m, which is related to the

initial volume fraction of pearlite (fP), and n are transformation related parameters given by:

0

1 ( )

1 ( ) ( )

A P

A P A P

m f f

m f f f f

(6.13)

0n

An n f

(6.14)

where m0, n0, and φn are constants.

128

6.2.1.3 Saturated volume fraction of austenite

If the steel is annealed at intercritical (α + γ) region, as discussed in Chapter 5, full austenite

formation cannot be achieved. Given sufficient soaking time, the volume fraction of austenite at

final equilibration is a function of the intercritical annealing temperature [43, 99, 104, 117]. For

the boron steel in this study, the phenomenological approach is employed in the development of

the transformation models for modelling. According to the experimental investigation in the

previous chapter, after isothermal soaking for 10-15 min at a chosen temperature, the growth rate

of austenite volume fraction becomes zero. Thus the saturated volume fraction of austenite, fAs at

that temperature can be modelled using:

21 3arctan ( 1)

As

As

C Tf C C

T (6.15)

where C1, C2, C3 and TAs are constants to be calibrated from experimental data.

The equations developed in subsection 6.2.1.2 are applied for full austenite formation in the γ

region. Adjustments are required to adapt the model for intercritical transformations. From

experimental observation described in the previous chapter, it was found that isothermal austenite

formation at different intercritical temperatures followed the same trend approaching

equilibration. Therefore, it is reasonable to substitute the item (1– fA

m) in equation (6.12), which

indicates the 100% austenite formation, with ( fAs

m– fA

m) (partial austenite formation). Then

equation (6.12) becomes:

(1 )

m m eA As A n

e

Vf f f

V

(6.16)

129

6.2.2 Formulation of unified constitutive equations

By introducing variables such as extended volume, saturated volume fraction, and volume

fraction of austenite, a set of unified constitutive equations, which are based on the mechanisms

of nucleation, growth and impingement, can be formulated to model the austenite formation in

the boron steel. For the convenience of discussion, the equation set is given first:

0 1 exp ( )

0 ( )

A NA P

A P

QN A AT f f

RT

f f

(6.17)

0 1 expB vQv B B T

RT

(6.18)

eV Nv (6.19)

(1 )

m m eA As A n

e

Vf f f

V

(6.20)

where

21 3arctan ( 1)

As

As

C Tf C C

T (6.21)

is the saturated volume fraction of austenite, and, the parameters m and n are defined as:

0

1 ( )

1 ( ) ( )

A P

A P A P

m f f

m f f f f

(6.22)

0n

An n f

(6.23)

where N and N are the nucleation rate and nuclei quantity of austenite per unit sample volume,

respectively; v is the volume growth rate of an austenite nucleus; Ve is the extend volume of

transformed austenite per unit sample volume, and its growth rate is modelled using equations

130

(6.19); fA is the volume fraction of austenite and its formation rate is expressed by equation (6.20);

m and n are parameters to characterise the impingement mechanism; R is the gas constant and T

is the absolute temperature; fp is the volume fraction of pearlite in the initial structure; A0, A1, φA,

QN, B0, B1, φB, Qv, C1,C2,C3, Tm, m0, n0, φn

are constants to be determined from experimental data.

The unified theory is used in this study for the development of the austenite formation model

consisting of multiple evolutionary equations. The variables in equations (6.17) – (6.20) have

their individual physical meanings related to the microstructural evolution during austenite

formation processes. The features and interactive effects of physical phenomena during the

transformation can thus be described. It is noted that the morphological parameters of the

material are merged and not counted individually in the equations, which allows the simplicity of

modelling work. But, in this case, a set of constants fits only a particular steel variant. Re-

determination of the constants is required when the initial microstructure of the steel is changed.

The materials model, equations (6.17) – (6.20), is a set of Ordinary Differential Equations (ODE)

in terms of time t, which can be solved with given initial values for the variables. Thus this is also

known as the solution for an initial value problem. In the numerical integration of solving the

equations, at 0t , 0N , 0v , 0eV and 2%Af for the starting temperature of 993K (further

explanation about this is given in subsection 6.2.3.1). Below this temperature, austenite formation

is not possible.

6.2.3 Determination of the equations

6.2.3.1 Calibration of the constants from experimental data

The model was calibrated by fitting the computed volume fraction of austenite to the

experimental results by adjusting the values of constants within the equations. The trial and error

method was adopted in the study.

131

The first step of calibration was to determine the constants from equation (6.21), where the

saturated austenite volume fraction fAs is a function of temperature. The values of the constants in

the equation are adjusted to get the best fit to the experimental points at 1023K, 1073K, 1123K,

and 1173K, as shown by symbols in Figure 6.1.

Figure 6.1 Comparison of experimental (symbols) and computed (solid curve) saturated volume

fraction of austenite at intercritical annealing temperatures using equation (6.21)

At the second step, the computation was conducted in an iterative and incremental manner.

Equations (6.17) – (6.20) were numerically integrated using the forward Euler method. The input

was initial values of the state variables and temperature profile. According to information

provided by the material supplier, Ae1 for the steel is 993K, at which about 2% of austenite

volume formation is visible. Therefore, the integration starts from 993K with fA = 2%. At the

same time, the initial values of N, v, and Ve are defined as zero, and fAs is given by employing

equation (6.21). The output was the integrated values of the variables. The evolution of fA was

used for fitting with experimental curves. The calibrated constants are listed in Table 6.1. Figure

6.2 shows the comparison of experimental (symbols) and computed (solid curves) volume

fraction of austenite formation with temperature and time under different heating rates and

0%

20%

40%

60%

80%

100%

873 973 1073 1173 1273 1373

Sa

tura

ted

vo

lum

n f

ra

cti

on

of

au

sten

ite, f A

s

Temperature (K)

132

soaking temperatures. Good agreements have been obtained and the features of experimental data

are exhibited clearly from the computed curves.

(a) Different heating rates (soaking temperature: 1173K)

(b) Different soaking temperatures (heating rate: 5K/s)

Figure 6.2 Comparison of experimental (symbols) and numerical integrated (solid curves)

volume fractions of austenite formation under different heating conditions for calibration

133

Table 6.1 Material constants for equations (6.17) – (6.23)

QN

(J/mol)

Qv

(J/mol)

A0 A1 B0 B1 φA φ

B Ae1

(K)

149000 40000 176000 2.2e5 9.2 9.2 1.4 0.12 993

C1 C2 C3 TAs

(K)

m0 fP n0 φn R

(J/mol·K)

36.0 1.2 0.475 1037 1.05 0.22 2.1 0.155 8.314

6.2.3.2 Validation and analysis

To validate the material model, a further computation was carried out using the determined

material constants listed in Table 6.1 for heating rate 2K/s, soaking at 1273K for 2min. As shown

in Figure 6.3, the predicted volume faction of austenite with temperature and time (solid curves)

both agree well with the experimental ones (symbols).

Figure 6.3 Comparison of experimental (symbols) and predicted (solid curves) volume fractions

of austenite formation for validation (heating rate: 2K/s, soaking temperature: 1273K)

134

Prediction of continuous heating transformation (CHT) diagram has great value for guiding the

design of heat treatment in practice. In Figure 6.4, the temperature and time to attain chosen

volume fractions of austenite (10%–70%) under continuous heating at different heating rates (1–

25K/s) have been predicted by using the determined model. The computed CHT data is

represented by solid curves. The data points which are available from experimental results are

provided in the figure as cross symbols. Most of the symbols lie on or close to the computed

curves, which again shows the reliability of the model. The predicted CHT diagram reveals that

the temperature to attain chosen proportions of austenite increases with increasing heating rate

and the effect is greater for higher austenite volume fractions; at a certain heating rate, the

temperature increment to increase austenite volume fraction by 20% is larger from higher

austenite volume fraction.

Figure 6.4 Comparison of experimental (symbols) and predicted (solid curves) continuous

heating transformation (CHT) data, which are shown for different volume fractions of austenite

(10%–70%) with various heating rates (1–25K/s)

993

1093

1193

1293

1393

0 20 40 60 80 100 120 140 160 180

Tem

pera

ture (

K)

Time (s)

25K/s

5K/s

2K/s

1K/s

70%

50%

30% 10%

135

Control of soaking time is of great significance in enhancing productivity and reducing cost in

practice. In Figure 6.5, the soaking time increments to attain 80%–90% austenite volume faction

at 1173K with different pre-heating rates (1–25K/s) have been predicted and summarised as a

solid line. The symbols are experimental data. Good agreement is shown again in this case. The

predicted trend indicates that for a chosen stage of transformation and a chosen soaking

temperature, less time is required for the steel preheated at a higher rate.

Figure 6.5 Comparison of experimental (symbols) and predicted (solid line) relationships of time

increment to attain 80%–90% austenite volume fraction under an isothermal condition (1173K)

with various heating rates (1–25K/s)

6.3 Viscoplastic-damage constitutive model

Viscoplastic constitutive equations are normally used to model the behaviour of metals that are

subjected to stress at elevated temperatures (normally T > 0.5Tm, Tm is melting temperature) or

deformed at high strain rates (normally ε > 100/s) [154]. In this section, a dislocation-based

viscoplastic-damage model based on the work by Lin et al. [155-157] is introduced. The unified

theory has been used for the development of the constitutive model consisting of multiple

evolutionary equations, through which the evolution rates of state variables, such as plastic strain,

10

100

1000

1 10 100

So

ak

ing

tim

e i

ncrem

en

t,

Δt

(s)

Heating rate (K/s)

136

normalised dislocation density, and damage are modelled. The equations are adopted in section

6.4 and expanded in section 6.5, to describe the deformation behaviour of boron steels observed

in the hot and cold tensile tests, respectively.

6.3.1 Flow rule

A flow rule normally describes the flow stress response to the rate and extent of plastic straining

for viscoplastic solids, incorporating factors such as initial yield, viscoplastic effects, and work

hardening.

For a rigid perfect viscoplastic solid, as shown in Figure 6.6 (a), the relationship between flow

stress, which is equal to viscous stress σv, and plastic strain rate εPcan be described by Norton’s

law [138]:

*( )

P nv

(6.24)

where λ* and n are temperature dependent material parameters. Although the equation was

originally formulated as an empirical fit, similar results have been obtained by studying the

motion of dislocations [158, 159].

(a)Rigid perfect viscoplasticity (d) Elasto-viscoplasticity with isotropic hardening

Figure 6.6 Flow stress-strain responses of viscoplastic solids

137

In practice, most metals and alloys show plastic yield and work hardening during straining. Thus,

as shown in Figure 6.6 (b), the flow stress σ can be taken as the sum of initial yield stress k equal

to the elastic limit, viscous stress σv representing the viscoplastic effects, and strain hardening H

caused by the interaction of dislocations, i.e. σ = k+σv+H [138, 155]. In this case, the σv in

equation (6.24) can be substituted by (σ-k-H)+, where the bracketed terms are used to indicate

that only positive results are valid [156]. The flow law is thus expressed as [61, 63]:

Vn

P o k H

K (6.25)

where 𝜀𝑜 is equal to 1 under tension and -1 under compression, K is a parameter related to

viscous stress, and nV is viscous exponent. A higher value of nV indicates a less variation in stress

for a certain change of straining rate, that is, the viscoplastic effects are weaker. When 𝑛𝑉 > 20,

the deformation behaviour of material is closed to plasticity [16, 160]. Both K and nV are

temperature dependent. They are given by Arrhenius-type equations (6.26) and (6.27),

respectively, indicating the reduction in viscous stress and increase in viscosity with increasing

temperature.

0 exp

KQK K

RT

(6.26)

0 exp

nV V

Qn n

RT

(6.27)

where K0 and nV0 are material constants, and QK and Qn are activation energy related to the

viscosity of material, R is the gas constant and T is the absolute temperature.

The initial yield stress k decreases as temperature increases, since the external energy required to

overcome obstacles to plastic straining decreases [161]. It is also expressed in the Arrhenius term:

138

0 exp

kQk k

RT

(6.28)

where k0 is a material constant, and Qk is the activation energy associated with initial plastic slip.

The hardening term H is formulated in terms of dislocation-based equations in the following

subsections.

6.3.2 Isotropic work hardening

The increased dislocation density due to plastic deformation raises the resistance of a metallic

material, and the material is thus work hardened. Lin et al. [61-63] used the equation below to

describe the isotropic work hardening as a function of normalised dislocation density:

RnH B (6.29)

where B is a temperature parameter given by:

0 exp BQB B

RT

(6.30)

where B0 is a material constant, and QB is the activation energy associated with hardening

mechanisms.

, termed normalised dislocation density, is used as a practical expression of the dislocation

state of material (further details are given in the following subsection) [156].

nR is hardening exponent. From Nes’s study [162], as the dislocation density increases, the

average distance that the mobile dislocations migrate before being stored (also called mean

dislocation free path, L) decreases. As a result, higher stress is required to continue plastic

straining. The mean dislocation free path (L) allowing for dislocation migration is governed by

the inverse square of the dislocation density (𝜌), i.e. L ∝ ρ -0.5; at the same time, the hardening

139

stress (H) is inversely proportional to the mean dislocation free path (L), i.e. 𝐻 ∝ 𝐿−1. Therefore,

the value of nR is theoretically suggested to be 0.5. However, refinement is needed for particular

materials and working conditions. The value nR = 0.4 was adopted by Cai for modelling boron

steels under hot stamping conditions [16].

Compared with the classical strain hardening law (H = Bεn) which is an empirical approximation

without physical base, the dislocation-based equations are capable of capturing the material

behaviour at the microscopic level. Although still termed hardening laws, equations (6.29) and

(6.30) can account for material softening from a reduction in the dislocation density. The

evolution of dislocation density and associated recovery mechanisms are introduced in the

following subsection.

6.3.3 Evolution of dislocation density

Lin et al. [62] summarised that two mechanisms contribute to net accumulation rate of

dislocation for a non-recrystallizing metal: trapping of dislocations during plastic slip and

annihilation of dislocations from recovery processes, i.e. ρ =ρStore

- ρRecover

.

A normalised dislocation density concept was defined by Lin et al. [61, 62] as ρ=1– ρ0/ρ, where

ρ0 is the initial dislocation density of material, and ρ is the instantaneous dislocation density

during deformation. The normalised dislocation density varies from 0 (the initial state) to 1 (the

saturated state of a dislocation network after severe deformation) [62]. Based on the definition, a

constitutive equation for the evolution of dislocation density has been proposed as [16, 62, 63,

141]:

21 PA C (6.31)

140

where A and γ2 are material constants, C is a temperature dependent parameter. The first term in

the equation represents the storage of dislocations during plastic slip and concurrent reduction in

dislocations due to dynamic recovery. Dynamic recovery is due to continuous reorganisation of

dislocations during deformation, which is in terms of dislocation climb at high temperature and

dislocation cross-slip at low temperature [62, 63]. By adopting the dynamic recovery term, the

normalised dislocation density can be limited to the saturated state of a dislocation network being

1 [62]. The second term in equation (6.31) represents the effects of static recovery. The static

recovery is a function of time and is favoured by thermal activation [19]. At elevated

temperatures, annealing can effectively remove dislocations from the matrix [16]. Thus this term

is normally taken into account for hot working conditions. To show greater effects for a higher

temperature, the parameter C is given as:

0 exp CQC C

RT

(6.32)

where C0 is a material constant, and QC is the activation energy associated with static recovery

mechanisms.

By using equations (6.31) and (6.32), the dislocation recovery mechanisms are manifested as a

decrease in the hardening at the macroscopic level [138]; the absolute values of dislocation

density are not required.

6.3.4 Evolution of damage

The damage concept has to be introduced to model the failure of materials, which is necessary for

the prediction of formability under hot forming conditions, and especially important for the load

bearing analysis in crash scenarios. By implementing damage evolution equations into elasto-

141

viscoplastic constitutive equations, ductility and reduction of flows tress in the late stage of

deformations can be predicted [139].

Damage mechanisms vary with the microstructure of materials and working conditions, the major

type of which for metallic materials have been summarised by Lin et al. [139]. In this study,

damage evolution under cold working conditions involves void nucleation, growth, and

coalescence [142]; the damage mechanism for hot stamping conditions is associated with both

ductile continuum void growth in grains and microwedge cracking at grain boundaries [139]. A

‘plasticity-induced’ ductile damage model, which has been proposed by Lin et al. [139] and

applied for both cold working and hot stamping conditions [16, 163], is given as:

3

1

P

(6.33)

where �� is damage evolution rate, which could be influenced by plastic strain rate 𝜀𝑃, flow stress

level 𝜎, and the development of damage 𝜔 itself. The value of 𝜔 lies in the range from 0 to 1,

indicating that the state of material changes from undamaged to completely failed. In practice,

metals fail at a damage value lower than 1. γ3 and φ are material constants providing flexibility to

the damage model. If the strain-rate-induced flow stress variation does not influence damage

evolution (manifested by strain rate dependency of ductility at the macroscopic level), 0 is given

to the value of γ3. β is given in terms of Arrhenius-type equation for hot working conditions:

0 expQ

RT

(6.34)

where β0 is a material constant, Qβ is the activation energy associated with damage mechanisms.

142

6.3.5 Modified flow rule and Hooke’s law

The damage term should be taken into account in the flow stress-strain relationship. Since the

imposed stress is sustained by a decreasing amount of load bearing material as damage

accumulates, the material is considered to be subjected to an augmented stress over the

undamaged area 1–ω, creating an effective stress of σ/(1–ω) for further plastic deformation and

damage evolution [156]. Thus, the flow rule of equation (6.25) is modified as:

1

Vn

P o

k H

K

If 0, 01

Pk H (6.35)

1 ( 0)

1 ( 0)

o

The deformation of a yielding solid with an imposed stress consists of reversible/elastic strain εE

and irreversible/plastic strain εP, i.e. εT= εE+ εP. From Hooke’s law, flow stress can usually be

related to elastic strain as: σ = E(εT– εP), where E is Young’s modulus of elasticity [138]. Again,

by taking the damage softening effects into account, the Hooke’s law is given as:

(1 ) T PE (6.36)

Young’s modulus E is temperature dependent, and difficult to determine at elevated temperatures

[156]. An Arrhenius-type equation used by Cai [16] for modelling boron steels are adopted here:

0 exp EQE E

RT

(6.37)

where E0 and QE are constants.

143

6.4 Unified viscoplastic-damage constitutive equations for boron steels under hot

stamping conditions

The viscoplastic-damage constitutive model introduced in the previous section is adopted to

account for the viscoplastic behaviours of the austenite and initial phase (78% ferrite and 22%

pearlite) of boron steel under hot stamping conditions. The values of material constants in the

equations corresponding to each phase state are calibrated from the respective experimental true

stress-strain data. Further analysis on the modelling results is made.

6.4.1 Formulation of unified viscoplastic-damage constitutive equations

Based on the mechanisms of dislocation-driven evolution processes such as hardening, dynamic

and static recovery and damage, linked with the experimental characterisation of the effects of

forming temperature and strain rate, a set of unified viscoplastic-damage constitutive equations

are listed below to model the thermo-mechanical response of boron steels:

1

11

1

Vn

P o

k H

K

If 0, 01

Pk H (6.38)

1 ( 0)

1 ( 0)

o

RnH B (6.39)

21 PA C

(6.40)

3

1

P

(6.41)

144

(1 ) T PE (6.42)

where the temperature dependent parameters are defined by:

0 expQ

k kRT

(6.43)

0 expQ

K KRT

(6.44)

0 exp

nV V

Qn n

RT

(6.45)

0 exp BQB B

RT

(6.46)

0 exp CQC C

RT

(6.47)

0 expQ

RT

(6.48)

0 exp EQ

E ERT

(6.49)

where R is the gas constant and T is the absolute temperature. Q, Qn, QC, QB, QE, Qβ, k0, A, B0, C0,

β0, K0, nV0, φ, γ1, γ2, and γ3 are constants to be determined from experimental data.

Equation (6.38) is the flow law, representing that plastic strain rate 𝜀𝑃 is a function of flow stress

𝜎, initial elastic limit 𝑘, and isotropic hardening H, with damage 𝜔 taken into account, where the

term 11 1

is adopted to provide the equation with higher flexibility. Equation (6.39) is the

isotropic hardening law formulated as a function of normalised dislocation density ��, where �� is

given by equation (6.40). The dislocation density evolution law (6.40) involves dislocation

accumulation, and dynamic and static recovery. Equation (6.41) is the evolution law of plasticity-

induced damage 𝜔. Equation (6.42) is a modified Hooke’s law. The unified equations (6.38) –

145

(6.42) are a set of non-linear ordinary differential equations that cannot be solved analytically. As

discussed in section 6.2, this type of equation set can be solved with given initial values for the

variables using numerical integration techniques.


6.4.2.1 Calibration of the constants from experimental data

The model has to be determined from fitting the computed true stress-strain curves to the

corresponding experimental results by adjusting the values of constants within the equations.

Two sets of values were calibrated for the austenite and initial phase of boron steels, respectively.

The forward Euler method was used for the numerical integration and trial and error was adopted

based on a deep understanding of the physical base of each state variable and material constant.

The real strain rates calculated from experimental results for each testing condition, instead of

designed values, were input to the numerical integration code to ensure the fitting accuracy. The

values of E0 and QE were determined from Young’s modulus values from literature [164]. For

computation efficiency, the damage ω = 0.7 was taken as the criterion for the failure of boron

steel. The reason is that the value of stress drops sharply with ω above 0.7, which requires tiny

time step for the integration and thereupon high computation cost.

The procedure to determine the material constants mainly consists of two steps (take austenite as

an example). At the first step, determine equations (6.38) – (6.42), by taking the temperature

dependent parameters k, K, nV, B, C, β, and E as constants, from fitting the true stress-strain data

for different strain rates, for a deformation temperature of 973K; At the second step, by keeping

the obtained values of k, K, nV, B, C, β, and E at 973K as well as other material constants in

equations (6.38) – (6.42) unchanged, adjust the 6 pairs of pre-exponent and activation energy

associated constants in equations (6.43) – (6.49) to fit the true stress-strain data for different

146

deformation temperatures, at the strain rate 0.3–0.5/s. More robust checking can be carried out by

using the constant values to predict further data sets.

The calibrated material constants for both the austenite and initial phase of boron steels are listed

in Table 6.2. Figures 6.7 and 6.8 are comparisons between experimental (symbols) and computed

(solid curves) true stress-strain curves for the austenite and initial phase, respectively. Good

agreement has been obtained for the austenite at all testing conditions, and for the initial phase at

different strain rates. An error for initial phase at different forming temperatures can be seen in

Figure 6.8 (b). This feature has been pointed out in the analysis of test results in Chapter 5

(subsection 5.3.2.2). It implies that the thermal-activated mechanisms described by Arrhenius-

type equations, which are normally applied for elevated temperatures (T > 0.5Tm, Tm is melting

temperature, about 1800K for boron steels), may not be suitable for a temperature below 823K,

for the boron steel. Further improvement of the model might be needed. However, the current fit

can still provide acceptable prediction of material behaviour.

147

Table 6.2 Material constants for equations (6.38) – (6.49) for the austenite and initial phase of

boron steels

Q

(J/mol)

Qn

(J/mol)

QC

(J/mol)

QB

(J/mol)

QE

(J/mol)

Qβ

(J/mol)

k0

(MPa)

Austenite 4000 50000 10000 24000 1400 8000 12.921

Initial phase 14800 1000 5000 27000 1400 7000 5.820

A B0

(MPa)

C0 E0

(MPa)

K0

(MPa)

R

(J/mol·K)

φ

Austenite 16 12.084 0.560 143800 31.354 8.314 10.5

Initial phase 0.248 12.224 0.213 150000 24.410 8.314 13.8

nV0 nR γ1 γ2 γ3 β0

(MPa-γ3)

Austenite 0.0185 0.4 3.4 1.55 0.5 5.996e-3

Initial phase 4.33 0.4 3.1 1.54 0 0.052

148

(a) Different strain rates (temperature: 973K)

(b) Different temperatures (strain rate: 0.3–0.5/s)


stress-strain curves for austenite at elevated temperatures

0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5

Tru

e s

tress

(M

Pa

)

True Strain

2.45/s

0.4/s

0.045/s

0.006/s

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5

Tru

e s

tress

(M

Pa

)

True strain

873K-0.3/s

973K-0.4/s

1073K-0.5/s

149

(a) Different strain rates (temperature: 923K)

(b) Different temperatures (strain rate: 0.35–0.7/s)


stress-strain curves for the initial phase at elevated temperatures

0

50

100

150

200

250

300

350

400

0 0.1 0.2 0.3 0.4 0.5 0.6

Tru

e s

tress

(M

Pa

)

True strain

3.2/s 0.7/s

0.1/s 0.01/s

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6

Tru

e s

tress

(M

Pa

)

True strain

723K-0.35/s

823K-0.5/s

923K-0.7/s

150

6.4.2.2 Analysis on the modelling results

A physically-based constitutive model, as a rationalised form to describe material behaviours,

can explicitly reveal the interrelationship of critical mechanisms which act to alter the flow stress

response. The analysis of the modelling results here can be mapped to the previous analysis on

the experimental results. Two examples are given below:

To facilitate the discussion, because the temperature dependent parameters express physical

mechanics more clearly in the constitutive equations than the pre-exponent and activation energy

associated constants, the values of temperature dependent parameters for austenite at the

temperature of 973K and initial phase at 923K are given in Table 6.3. As discussed in Chapter 5,

the initial phase is more strain rate sensitive in viscous stress at 923K than austenite at 973K.

This is illustrated by the higher value of K (167.891MPa) and lower value of nV (4.933)

corresponding to 923K for the initial phase, compared with 51.405MPa and 8.934 corresponding

to 973K for austenite. Also, it was found in Chapter 5 that austenite shows more pronounced

static recovery, which is manifested by the higher value of C (1.927) corresponding to 973K for

austenite, compared with 0.409 corresponding to 923K for the initial phase.

Table 6.3 Temperature dependent parameters for the austenite and initial phase of boron steels

T

(K)

k

(MPa)

K

(MPa)

nV C B

(MPa)

E

(MPa)

β

(MPa-γ3)

Austenite 973 21.184 51.405 8.934 1.927 234.681 170965 0.016

Initial phase 923 40.030 167.891 4.933 0.409 412.108 180016 0.129

Analysis of the modelling results can assist further understanding of the mechanisms involved in

deformation, and in turn proves the reliability of the model.

151

6.5 Unified viscoplastic-damage constitutive equations for multiphase boron

steels for crashworthiness analysis

In this section, the viscoplastic-damage constitutive model introduced in section 6.3 is expanded

by using a phenomenological approach to take the phase composition of material into account, so

that the deformation behaviour of boron steels having various microstructures can be modelled

by one single equation set. The model is capable of describing the mechanical response of boron

steels being subjected to high strain rates at room temperature, which is analogous to crash

situations in automobiles. The material constants of equations are calibrated from experimental

data.

6.5.1 Formulation of unified viscoplastic-damage constitutive equations

Taken all temperature dependent parameters as constants, the viscoplastic-damage constitutive

model can be tailored to describe the deformation behaviour of a material at room temperature.

The formulation of unified constitutive equations is listed as below:

1

Vn

P o

k H

K (6.50)

If 0, 01

Pk H

1 ( 0)

1 ( 0)

o

1 PA

(6.51)

RnH B (6.52)

152

1

P

(6.53)

(1 ) T PE

(6.54)

Regarding the dislocation density evolution law (6.51), no static recovery is taken into account

for cold working conditions.

Based on this equation set, a set of values of material constants k, K, nV, A, B, 𝛽, and φ can be

determined for any phase state of the boron steel. In order to integrate the microstructure factor

into the model, so as to describe the continuum deformation of a boron steel part having graded

microstructure, constants k, K, A, B, and 𝛽 are expanded to phase composition dependent

parameters, in terms of functions of martensite volume fraction as below:

0 exp( ) x Mk k k f (6.55)

0 x MK K K f (6.56)

0 x MA A A f (6.57)

0 0 exp( ) x M x MB B B f k k f (6.58)

0 1

0 1 2

( 60%, 95%)

(1 ) ( 60% 95%)

x M M M

x x M M M

f f f

f f f (6.59)

where fM is the volume fraction of martensite phase, k0 and k

x are yield strength associated

material constants, K0 and K

x are viscoplasticity associated material constants, A0 and A

x are

dislocation density evolution associated material constants, B0 and B

x are work hardening

associated material constants, and β0, β

x1, and β

x2 are damage associated material constants.

Equations (6.55) – (6.59) are formulated based on the experimental analysis in Chapter 5

(subsection 5.4.2.2: the effects of fM on the mechanical properties of boron steels), by using a

153

phenomenological approach. For example, the yield strength k adopts the exponent fit with fM;

the damage associated parameter 𝛽 is given as a piecewise function, describing the low ductility

of the steel corresponding to fM = 60%–95% separately.

Assuming that the phase composition dependent parameters don’t change with strain rate,

equations (6.50) – (6.59) can be formulated as a unified constitutive equation set, capable of

modelling the dynamic deformation behaviours of boron steels having various phase

compositions.


The material constants in equations (6.50) – (6.59) are determined by fitting the computed true

stress-strain data to experimental results. Again, the non-linear ordinary differential equations

were solved in terms of numerical integration by using the forward Euler method. The trial and

error method was adopted.

The procedure to determine the material constants mainly consists of three steps. First, a

preliminary calibration of k0, K

0, A

0, B

0, β

0, nV, and φ is undertaken by fitting true stress- strain

data for the initial phase (fM = 0%) at different strain rates. Second, kx, K

x, A

x, B

x, and 𝛽

x1 are

calibrated by fitting true stress-strain data for the full martensite phase (fM = 100%) at different

strain rates (Note: the value of kx is determined by referring the experimental fit in Figure 5.22,

necessary refinements for k0, K

0, A

0, B

0, β

0, nV, and φ are made). Last, 𝛽

x1 is refined and 𝛽

x2 is

determined by fitting true stress-strain data for boron steel having different volume fractions of

martensite, at a strain rate of 0.001/s.

The determined material constants for boron steel are listed in Table 6.4. Figure 6.9 shows a

comparison between experimental (symbols) and computed (solid curves) true stress-strain

154

relationships for boron steel with various phase compositions. Good agreement can be seen for

all three groups of data.

(a) Different𝜀 for initial phase (fM = 0%) (b) Different 𝜀for martensite (fM = 100%)

(c) Different martensite volume fractions, fM (strain rate: 0.001/s)


stress-strain curves for boron steels with various phase compositions at room temperature

0

200

400

600

800

1000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Tru

e s

tress

(M

Pa

)

True strain

50/s 5/s

0.001/s

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1

Tru

e s

tress

(M

Pa

)

True strain

500/s 5/s

0.001/s

0

200

400

600

800

1000

1200

1400

1600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Tru

e s

tress

(M

Pa

)

True strain

100%

88.5%

61.3%

19%

0%

155

Table 6.4 Material constants for equations (6.50) – (6.59)

k0

(MPa)

K0

(MPa)

A0 B

0

(MPa)

β0 φ nV E

(MPa)

131.5 134.0 10.0 805.5 0.615 10.0 8.0 205000

kx K

x

(MPa)

Ax B

x

(MPa)

𝛽x1

𝛽x2

nR

1.27 -10.0 58.0 792.0 0.431 0.5 0.5

6.6 Summary

An austenite formation model has been developed. It is able to characterise the phase

transformation process of the boron steel under both non-isothermal and isothermal conditions,

where the effects of heating rate and soaking temperature on the austenite formation are

rationalised. A viscoplastic-damage constitutive model is introduced. It has been adopted to

model the thermo-mechanical properties of boron steels in both the austenite and initial phase

states under a range of forming temperatures and strain rates; it has also been tailored and

expanded to describe the deformation behaviour of boron steels with various phase compositions

under a wide range of strain rates appropriate for impact crashworthiness applications. All the

models have been determined from test results in Chapter 5. Good agreement between each set of

experimental and predicted data has been obtained.

156

CHAPTER 7 CONCLUSIONS AND SUGGESTIONS

FOR FUTURE WORK

7.1 Conclusions

Hot stamping of UHSS panels with graded microstructure is a promising technology to better

meet safety and light weight requirements in automotive applications. A selective heating and

press hardening strategy, to grade the microstructural distribution of a press hardened component

by selectively heating the blank prior to forming, has been proposed and validated in this study.

To enable effective process control of the hot stamping process for forming a part with optimised

functional performance, comprehensive understanding and fundamental material models of the

austenite formation and deformation behaviour of boron steel under hot forming conditions, as

well as the dynamic response of a press hardened part with tailored properties in collision

situations, have been developed, based on experimental investigations and mechanism studies.

Further conclusions associated with four main aspects of the study are summarised in the

following four subsections.

7.1.1 Feasibility of the selective heating and press hardening strategy

The selective heating and press hardening strategy has been successfully implemented in a hot

stamping operation. Demonstrator parts, with different microstructural topographies, have been

formed in good qualities without visible spring-back. Microstructural distributions in as-formed

parts have been exhibited by hardness testing and SEM microscopy. The structural performance

of as-formed parts under three point bending has been determined. Based on experimental results,

the following conclusions have been drawn:

157

Differentially heated blanks can be press hardened with high shape quality, which is

essential for commercial viability of the forming process.

Microstructural distribution in formed parts can be graded by the design of thermal

conditions, which provides the basis for optimising structural properties of a part.

The deformation mode of a part can be adjusted through microstructural arrangement; the

energy absorption capacity of a part can be improved through advantageous combination

of strong and ductile regions. Thereby, the potential of the selective heating and press

hardening strategy in functional optimisation is demonstrated.

7.1.2 Austenite formation in boron steel during selective heating

Heat treatment tests were performed to study the formation of austenite in boron steel during

selective heating in hot stamping processes. From analysis of the test results, the effects of

heating rate and temperature on progress of austenite formation under both non-isothermal and

isothermal conditions were investigated, and the following conclusions have been drawn:

During the heating step, to attain a given volume fraction of austenite, a higher

temperature and less time are required for a higher heating rate. Both temperature and

time follow a linear relationship with heating rate, when plotted on logarithmic

coordinates. The effects of heating rate are greater on temperature but less on time, for

increasing austenite formation.

The influence of heating rate remains at the same level in the subsequent isothermal

(soaking) step. The time to attain given volume fractions of austenite (80%–85%, 85%–

90%, and 90%–95%) all follow a linear relationship with heating rate, when plotted on

logarithmic coordinates. During soaking, equilibrium can be approached in a shorter

period when the heating rate is higher.

158

For austenite formation during intercritical soaking situations, equilibrium can be

approached in shorter period when the temperature is higher. The logarithm of time to

attain a certain percentage of saturated austenite volume fraction, 80% fAs–90% fAs at a

chosen temperature, follows a linear relationship with inverse temperature.

Regarding isothermal austenite formation, following a given heating rate or temperature,

all evolution curves of normalised austenite volume fraction (fA/fAs) follow the same form

and approach equilibrium on a normalised time scale. This shows the mechanisms

controlling transformation do not change with conditions, in the range of heating rate and

temperature considered.

An understanding of the austenite formation process can significantly benefit

optimisation of thermal conditions in hot stamping practice and the empirical relations

extracted through the analysis can provide useful information for material modelling.

A physically-based austenite formation model has been developed to describe the formation of

austenite in boron steel under selective heating conditions. The equations are formulated based

on three austenite formation mechanisms: nucleation, growth and impingement. The evolution

rate of state variables, such as extended volume, saturated volume fraction, and real volume

fraction of austenite, are modelled. The data from heat treatment experiments were used to

calibrate and validate the equations. Further conclusions are listed as follows:

The austenite formation under both non-isothermal and isothermal conditions can be

described; the effects of heating rate have been taken into account for the subsequent

isothermal transformation.

Both full and partial austenite formation at γ and (α + γ) regions can be modelled.

159

The determined model gives accurate predictions of the austenite formation progress,

which is validated from experimental data.

7.1.3 Thermo-mechanical properties of boron steel under hot stamping

Hot tensile tests were performed to study the thermo-mechanical properties of the austenite and

initial phase (78% ferrite and 22% pearlite) of boron steel. From analysis of the test results, the

following conclusions have been drawn:

For both the austenite and initial phase of the boron steel, pronounced viscoplastic

properties at elevated temperatures have been observed: the stress level increases with

increasing strain rate and decreasing temperature; also, ductility decreases with

decreasing temperature. The strain rate effect on ductility is significant for austenite, but

negligible for the initial phase.

The strain rate dependence of flow stress (at true strain levels of 0.005, 0.05, and 0.1)

approximates closely to a power law for both phase states. The temperature dependence

of flow stress (at true strain levels of 0.005, 0.05, and 0.1) follows closely the Arrhenius

activation energy equation for austenite.

A viscoplastic-damage constitutive model, which takes the mechanisms of dislocation-driven

evolution processes such as hardening, dynamic and static recovery and damage into account, has

been adopted to describe the deformation behaviour of the austenite and initial phase of boron

steel under hot stamping conditions. The values of material constants in the equations

corresponding to each phase state have been calibrated from the respective experimental true

stress- strain data. Further conclusions are listed as follows:

The effects of temperature and strain rate on the thermo-mechanical response of boron

steel are taken into account in the model.

160

The damage evolution and material failure can be modelled.

The predicted stress-strain data show good agreement with the experimental results for

the austenite at all testing conditions and for the initial phase at different strain rates.

Although the fit for the initial phase at different temperatures has a small deviation, it can

still provide acceptable prediction of the tensile behaviour.

7.1.4 Mechanical properties of boron steel with various microstructures at room

temperature

Dynamic and quasi-static tensile tests combined with hardness testing and microstructural

observation were carried out to study the mechanical properties of press hardened boron steel

with various microstructures at room temperature. Based on the test results, the strain rate

sensitivity of the martensite and initial phase of boron steel was analysed; the relationships

between mechanical properties and phase composition for boron steel with various

microstructures were rationalised. The conclusions are given as follows:

Both the martensite and initial phase of the boron steel exhibit viscoplastic properties

over a large range of strain rate (more than 5 orders of magnitude change). Initial phase

shows higher strain rate sensitivity than martensite.

With increase of martensite volume fraction in the boron steel, the hardness and true

ultimate tensile strength increases proportionally and the value of 0.2% proof stress

increases exponentially. A range of phase compositions for fM = 60%–95% corresponding

to dramatically reduced ductility of the steel has been identified.

The deformation behaviour of boron steel having various microstructures has been modelled by

one single viscoplastic-damage constitutive equation set. The set was developed by expanding a

physically-based viscoplastic-damage model through phenomenological approaches. The values

161

of material constants in the equations have been calibrated from experimental data. Further

conclusions are listed as follows:

The effects of phase composition, in terms of martensite volume fraction, on the

mechanical response of boron steel have been taken into account in the model.

The model is capable of describing the mechanical response of boron steel being

subjected to high strain rates (up to 500/s) at room temperature, which is analogous to

collision situations in automobiles.

Good agreement between experimental and predicted stress-strain data has been achieved.

7.2 Suggestions for future work

Forming limit

The damage evolution in material is usually associated with stress state and strain path [156, 165].

Taking these factors into account enables better prediction of material failure, which is important

for evaluating the forming limit of boron steel under hot stamping conditions. Therefore,

improved modelling in the viscoplastic-damage models is recommended. Correspondingly,

experimental work, such as biaxial tensile testing, to obtain more comprehensive fundamental

data is necessary.

In the selective heating and press hardening process, multiple phases of boron steel are subjected

to hot deformation. Both the constitutive deformation behaviour of austenite and untransformed

initial phase are modelled in the current study, and it is reasonable to calculate the flow stress

response in a multiple phase area using linear interpolation by knowing the volume fractions of

each phase. However, damage evolution in the multiphase boron steel during hot deformation

was not significantly investigated. A further study on this can be done to realise a more accurate

162

prediction of material failure at transition zones. This is important for identifying the application

scope of the selective heating and press hardening process, in terms of part complexity.

Phase transformation during quenching

Although significant knowledge on the phase transformation of boron steel during cooling is

available in literature, all conclusions and material models are based the decomposition of a full

austenite. With respect to the selective heating and press hardening process, the phase

transformation of boron steel at transition regions involves austenite decomposition from

multiple phase states. The influence of the other phase, ferrite, on the transformation has not as

yet been identified. Investigation of this can help to identify the critical cooling rate for

martensitic transformation, which is an important parameter in industrial production.

Process simulation for function-driven-optimisation

The fundamental material models developed in this study allows the function-driven-optimisation

concept to be realised. In the next stage, process simulation can be carried out by using FE

commercial software, such as LS-DYNA, with the implementation of the material models via

user defined subroutines.

Under given thermal conditions, the austenite distribution in a boron steel blank prior to forming

can be predicted by simulating the selective heating process using the austenite formation model.

Subsequently, the blank, with the information of austenite volume fraction and temperature for

each element, is subjected to hot stamping in the thermo-mechanical simulation, where the

deformation behaviour of the blank is described using the viscoplastic-damage model of boron

steel at elevated temperatures. Provided the quenching rate is sufficient for complete martensitic

transformation, the martensite distribution in the as-formed part can be known from austenite

distribution. Then, the achieved part is used as an input model for functional assessment

163

simulation (such as crash), using the viscoplastic-damage model of boron steel at room

temperature. By taking the information of martensite volume fraction and thickness for each

element into account, the performance of the part is allowed to be predicted accurately. A

successful simulation of the whole process will enable a proper selective heating condition to be

determined for optimising structural properties of a part.

164

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177

APPENDIX 1 CALCULATION OF AUSTENITE

VOLUME FRACTION

A method has been developed to calculate the volume fraction of austenite from the

experimentally measured ΔW. Referencing the natural strain definition, the relative volume

change during the thermal-expansion/contraction and phase transformation can be expressed as:

0

lnV

vV

(A1.1)

where V0 is the initial volume of the specimen, and V is the volume at any time during the thermal

cycle.

Assuming that the specimen expands isotropically, i.e. 𝑣 = 𝑊3, the relative volume change can

thus be related to ΔW as follows:

0 0

3ln 3ln( 1)

W W

vW W

(A1.2)

Based on Equation (A1.2), the width change curve can be converted to a relative volume change

curve. An example, for the test condition of heating rate 5K/s and soaking temperature 1173K, is

given in Figure A1.1.

178

(a) The width change against temperature

(b) The relative volume change against temperature

Figure A1.1 Conversion from width change curve to relative volume change curve

0

0.02

0.04

0.06

0.08

0.1

0.12

873 973 1073 1173 1273

Ch

an

ge

of

wid

th, Δ

W (

mm

)

Temperature (K)

179

Regarding the pure thermal expansion and contraction stages, the following relationship is

proposed:

0 0( ) ; ( ) v T v C T v T v C T (A1.3)

where vψ0 and vψ (T) are the relative volume change of the initial phase (ferrite and pearlite mixed

microstructure, represented by ψ in this study) at 873K and any temperature T, respectively. vγ0

and vγ (T) are the relative volume change of austenite phase (γ) at 873K and any temperature T,

respectively. ΔT is the temperature increment from 873K. Cψ and Cγ are the thermal expansion

coefficients of the material with the initial phase mixture and austenite. Corresponding to the

slopes of the linear regions in Figure A1.1 (b), they have been measured as: Cψ = 4.41056 × 10-5

/K, Cγ =6.82215× 10-5 /K.

Regarding the phase transformation stage, the relative volume change, which is the function of

both temperature and time, can be given as:

( , ) (1 ) ( ) ( )A Av T t f v T f v T (A1.4)

where fA is the volume fraction of austenite. Thus the extent of phase transformation can be

calculated as:

( ) ( , )

( ) ( )A

v T v T tf

v T v T

(A1.5)

where vψ (T) and vγ (T) are calculated according to equation (A 1.3), and v (T, t) is obtained from

the relative volume change-temperature curve in Figure A1.1 (b). Based on Equations (A1.2),

(A1.3), (A1.5), the dilatometric curves can be transformed to austenite volume fraction curves.

180

APPENDIX 2 STRAIN CORRECTION AT NECKING

STAGE

For tensile testing, when failure doesn’t occur at the specimen centre section where the

dilatometer is clamped, the strain obtained from dilatometer measurement cannot accurately

present the deformation behaviour of specimen after onset of necking. Therefore, a method has

been defined to correct measured strain data to represent that at the necking position.

Figure A2.1 schematically shows the longitudinal area of interest between the centre section and

failure section of a tensioned specimen. At the time just before onset of necking (at the peak

load), the area has a rectangular shape (light grey). The specimen width and the distance between

centre section and failure section are Wc0 and l0, respectively. When localised deformation takes

place, the shape of the area deviates from rectangular, and in this method, it is simplified as a

trapezium: the trapezium drawn in dashed lines represents an instantaneous shape during necking,

where the widths of centre section and failure section are Wci and Wfi, respectively, and the

distance between centre section and failure section is li; the trapezium in dark grey represents the

final shape of the area when the specimen fails, where the corresponding dimensions are Wcn, Wfn,

and ln. The angle 𝛼 represents the deviation of specimen edge from its original direction. It equals

zero in the beginning, and for a constant strain rate, it is assumed to increase proportionally with

time during necking.

The target is to map the evolution of Wci to Wfi, thus the corrected true strain at necking stage can

be given by:

0

2ln( ) fi

T

W

W (A2.1)

181

where W0 is the initial width of specimen. The calculation of Wfi is given in detail as follows:

Figure A2.1 Strain correction method at necking stage

The instantaneous width of the failure section Wfi can be formulated as:

2 tan fi ci i iW W l (A2.2)

where Wci is obtained from dilatometer measurement, and

0 0( ) i n

il l l l

n (A2.3)

i n

i

n (A2.4)

where n is the total number of time intervals for the necking stage in data acquisition, i represents

an instantaneous time interval.

182

Regarding equation (A1.2), l0 is given by:

00 n

n

Sl l

S (A2.5)

where S0 and Sn correspond to the strokes (data from Gleeble data acquisition) at the onset of

necking and failure, respectively. The value of ln can be manually measured from the fractured

specimen.

Regarding equation (A1.3), the final angle αn can be calculated by:

arctan2

cn fn

n

n

W W

l (A2.6)

where Wcn is read from dilatometer measurement, Wfn and ln are manually measured from the

fractured specimen.

Figure A2.2 is an example showing the true stress-strain curves before and after correction. A

correct failure strain and improved flow stress accuracy can be ensured by using the method.

Figure A2.2 An example true stress-strain curve showing the correction at necking stage

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4

Tru

e s

tress

(M

Pa

)

True strain

Dilatometer measured data

Corrected data

Strain error

at failure

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